How does the Spirit empower us? He awakens ⁶our spirit by revealing to us His beauty, majesty, and glory, which arouses in us affections/love/longing for Him.
This grows over time as we see more and more of God's glory (2Co 3:18). The more clearly we see Him in all His glory, the more our love, trust, and obedience grows i.e. the more we are moved/empowered by the Spirit of God's infinite love to pursue and follow Him.
Why does our beholding God in his glory arouse affection?
Because God is all glorious (beauty, majesty, worth) and we are in His image, created to see and experience our own glory in seeing His. This, in large part, means we are relational beings just like God is, who from all eternity past has exchanged honor, adoration, and love between the Father and Son in, by, through the ¹Spirit.
But what does this have to do with our capacity for affection? To answer this, we must first know what God is like.
We are told God is love. This begs the question of what exactly is love, and why is God this way?
Let's break it down.
Love is essentially valuing something to such an extent that it stirs up affection for that which is valued. We are attracted to what we value/adore/cherish most. The reason affections are stirred is that the object of our love/affections matches up with and meets in us our desire and need for being valued and loved.
To be able to value something (God in this case) we must have the capacity to value it (Him). There must be a corresponding quality in us that matches who He is that enables us to enjoy his infinite glory/value i.e. our own sense of glory/value as bearers of His image - i.e. His likeness.
This is true of us because it is true of God first, and we are in His image i.e. it all starts with God. We are the way we are because God is the way he is.
God is the most valuable, worthy, glorious, beautiful being over and above all other beings/things. In fact, everything beautiful comes from and is sustained by Him. Nothing that is, exists without God, including - and especially - you and I.
The Son who emanates from this most beautiful God and Father is the Father's express (exact) image, Heb 1:3; Col 1:15; John 14:6-10. i.e. His only begotten -- eternally imaged forth -- Son. Throughout eternity, there has always been the Father and the perfect imaging forth (logos) of the Father's beauty, majesty, and worth - i.e. the Son - and the perfect affection of the Father for the Son and the Son for the Father, issuing forth as the Spirit.
This means the Son is equally valuable, worthy, glorious, and beautiful as the exact representation and perfect image of this all-beautiful God, who is also Father. To say it succinctly, Christ is God the Son.
Now as the Father beholds this exact and ¹perfect image of himself, He gazes upon and delights in this image - i.e. His Son - and values Him above all else -- since God is most valuable and values Himself about all things -- there is no one else more beautiful, majestic and worth adoring than the majestic and glorious God, resulting in affections for His perfect image of Himself (i.e. Christ) who is equally most valuable, worthy, glorious, beautiful and equally God.
God, being most valuable and worthy of adoration, loves the perfect image of Himself, his only begotten Son, resulting in praise, adoration, joy, and happiness by the Father for His Son as He beholds His Son's beauty, majesty, and glory.
His Son, in turn, responds back to the Father, who is the most valuable, worthy, glorious, beautiful source of love and life, reflecting this love back to him.
This is referred to by many past (and some present) theologians as the beatific vision of God i.e. a vision of delight in loving/valuing the most lovely/beautiful. This creates affections of joy, delight, pleasure, bliss, and happiness in beholding that which is most valuable/beautiful/ glorious, etc. Just think of the first time you "fell in love," except it only grows with time and a greater beholding.
This beatific vision is so passionate and "solid" that it issues forth into the distinct, separate, and eternal person of the Spirit (the eternal passion/love/affection) of God (Jonathan Edwards addresses this possibly more than other past theologians). Each of these persons - Father, Son, and Spirit - is one in essence (i.e., one God), yet ²distinct in their function/role.
The Spirit of God is the very Spirit of passion and love expressed between the Father and Son as they gaze upon and behold the beauty of the other, i.e., they experience a beautific vision of the other. The Spirit of God is the manifestation (passion) of this beholding and the very heart of who God is. God is Spirit and He is love i.e. both. These characteristics or qualities are the very essence of God and are inseparably connected, if not synonymous (though they are distinct and separate at the same time, as mentioned above). God is Spirit (passionate love), and passionate love (the Spirit) is God.
For us to behold and enjoy this beautiful God, we too had to be like God with the ability to behold and enjoy him in all his glory in the same way the Father and the Son behold, love, and value each other. As God's created image-bearers (vs His Son, who is the only eternally begotten image-bearer), our sense of perfect value, worth, and glory is bound up in and dependent on beholding and participating in God's perfect value, glory, majesty, etc. In this way, we are exactly like God, i.e., we are beings whose very essence is to partake of, experience, and enjoy perfect, infinite love, i.e., God Himself.
Yet, we have a problem
Because we are designed for the infinite, all-glorious God, when we turned away in the garden -- and still do -- and stepped out in rebellious independence from God, we disconnected (broke away) from him, the very Source of life and love. This left an infinite void or vacuum within each of us. We died spiritually i.e. our beholding, receiving, participating in, and responding to the God of infinite love and beauty was severed and lost.
We turned away from God. It was not God who turned away and rejected us. We rejected him (and still do), thereby cutting ourselves off from Him and our partaking of his infinite love, life, and beauty. We no longer experience the joy and bliss of participating in the unobstructed ³love and life of God. Our connection (relationship) was severed -- or more correctly, we pulled away and severed it (broke it...we died spiritually) by pulling away from God in rebellious independence -- attempting to be our own god (the lie of the serpent) and seeking to be our own self-sustainer if you will.
But our capacity for enjoying love and life was not lost. In other words, we are still designed for, desire, and need infinite love. This is who we are; these desires/needs did not disappear. They still exist and are fully intact. This is evident by our constant effort to replace this missing love and fill it with something, usually anything "within our reach" other than God.
Why?
We can't control God -- He is God after all -- but we think we can control the creation, which includes our fellow creatures. We try to use the wonderful gifts of God to sustain ourselves and our independence from God. We are rebels to Him and his original design of our being gloriously dependent on Him and in perfect union with Him.
We can not operate without a sense of value, love, relationship, meaning, purpose, etc. We are made for love (i.e. God) and therefore must have love. It is hard-wired into our makeup by God himself. To use a biblical description, we are made in his image...we are like God - who is the "first cause" of all things - that gives and receives love and extends it to others who are like Him. So much so that when someone feels totally worthless - or loses ⁴hope of experiencing a sense of value/meaning/love - they seek to end their life.
Absent the true and lasting Source of life and love, we now seek to meet that need and desire in or through created things instead of the Creator of those things - we reject the Creator and no longer directly (consciously) receive love and life from the only One who is the true and only Source of love, life, and all things. We go for the next best thing, ⁵his creation (Rom 1:20-23). This includes our fellow image bearers.
We now have an infinite (insatiable) void from the absence of infinite love, i.e., God himself -- which explains why we are ever seeking to fill it. All our efforts are now an attempt to replace the Source of this infinite love, now absent/missing (and missed), with whatever we can "get our hands on," i.e., creation, including other image bearers. Not just creation externally, but we use the gifts within us; our skills and talents, as well as the capacity (our 5 senses) to experience and enjoy the external joys and beauties of the creation all around us. We attempt to use anything and everything in creation, within and without, to fill the void of God's absence.
Our longing for love is infinite because our capacity for love is infinite. And our capacity is infinite because the source - i.e. God - of that capacity designed to fill it is infinite.
So, back to the original question. How does the Spirit empower us?
When the infinite love of God comes to dwell within us again as His Spirit, he reveals to us the beauty of God -- demonstrated in and through Christ, awakening and stirring up our love (affections) for Him again. We are fully and perfectly restored back to His infinite love through the work and the grace of Christ. The more the Spirit reveals God's beauty, the more we are stirred up and attracted to him. The more we are attracted, the more we desire him and are moved (empowered) to pursue him in faithful obedience, causing us to experience Him in his infinite love even more. This increases more and more as we draw nearer in increasingly greater faithful pursuit of him i.e. in loving, trusting obedience. And this, in turn, fills us - i.e. his love/Spirit fills us - so we desire others to have what we have. We want others to know this God and his infinite love, too. When filled with love, we are hard-wired to share it. This too is part of being in his image...the desire to pour forth love in the same way God does -- which we also do when we are filled with love - His Spirit. 
In short, the love of God poured out in us by the Spirit of God moves (empowers) our faithful pursuit of God, who calls us to share this with his other image-bearers as well as all of creation.
For a discussion on being transformed by God's glory, click here.
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¹ i.e. in, by, and through Love. God is Spirit and He is love. This is who He is, not what he does. What he does flows forth from who he is. We could say God is passionate, spirited, love.
²We too are in God's image. However, unlike Christ, who is the perfect and eternal image of God, we are created image-bearers. Nevertheless, just as God values the image of himself in Christ, so too he equally values his image in us.
³So much so, I would argue they are distinct in their understanding and will (awareness of self as a distinct being and in their awareness of the others). Not having different or opposing wills and understanding, but simply their own. They are in perfect harmony regarding what they will because they are one and the same God.
⁴Some argue that the life of God is the love of God and vice versa i.e. That which enlivens and moves God in all He is and does is his love. God's life consists of the love between the Father and Son, expressed and bound together by the Holy Spirit (the Holy Passion of God).
This is also suggested in Christ's prayer in John 17 and particularly verses 1-5; glory being the manifest display of this love and life.
⁵For a further discussion on hope, click here.
⁶This includes our own created, God-given internal abilities to secure and utilize the external creation all around us in an effort to fill the void left by God's absence.
⁶What is the essence of our spirit? Our sense of value, dignity, and worth as God's image bearers? When we experience these, we come to life i.e. Our spirit becomes alive. It is revived.
