where do we get the strength for self denial?

Where do we get the strength ¹to deny ourselves? To do things well for ²others - i.e. to love our neighbor as we love ourselves - requires extraordinary strength.

Why? Instead of focusing on our own needs and indulging in ³self-affirming and self-comforting behavior, our focus is on the ⁴needs of another. This clearly is not easy. On our own, without outside aid, it is not possible long term and difficult at best short term.

Denying ¹ourselves can only occur when we look to God for strength through increasing trust and dependence on Him.

What is it exactly we are asked to believe/trust in and how does this give us strength?

We must recognize/believe in our worth, significance, value to God, etc. i.e. we see ourselves as valuable because we know/believe God sees and feels this way about us. Our sense of value is not based on our own estimation, our circumstances, how we feel, or how others treat us but on how God views us i.e. as his infinitely beloved child. The evidence of His love is sending Christ to do all that we necessary to fully restore us back to Him. It is by believing this is God's view and posture towards us that we draw strength. Therefore, God himself and His disposition of infinite love toward us, is the source of our strength.

The essence of the strength necessary to deny ourselves is believing we are significant, loved, important, etc to God. When we really and truly “buy-in” to this, we no longer need to affirm ourselves by doing things to gain approval-acceptance. We know we are already affirmed. Now we do things because we already have affirmation, not in order to gain it. And not just a limited and temporary affirmation but an infinite and permanent affirmation by God Himself, who is the only infinitely and eternally valuable being in the universe. There is no greater affirmation then that which comes from the infinitely valuable i.e. God himself.

What exactly is the nature of this strength? In a word, it is simply knowing I am valuable to the God of infinite worth. When we fully grasp and believe this, nothing else matters. Or to say it as Paul does, if God is for us, who can be against us.

We are called to abide -- firmly remain standing -- in this belief and awareness of God's love/value for us. We are told by Christ himself to never lose sight of our being cherished and precious to him.

"As the Father has loved me, so have I loved you. Abide -- continually remain -- in my love." John 15:9

How can we be certain God feels this way about us? He not only tells us but demonstrated it by actions. Looking intently into what He and His Son put themselves through and denied themselves of to restore us back to them in their infinite love is our proof and reminder. This is why we do communion regularly, to remember the actions that Christ took on our behalf.

For a further discussion on why the value of the one who values us matters click here. 

For a discussion on why God loves the unlovely, click here. 
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¹we - self - still need to be nourished if you will, emotionally and spiritually, but not through self effort but in and through God.

Denying our self and death to self are tied together. There is no death to self without denying our self and to deny our self results in death of self. Death to self is not literal or absolute i.e. we –self– don't die but we die to self loving, self comfort and self-sustaining behavior/actions.

Nor is death to self, devaluing ourselves, it is knowing our true value is in Christ and loving others out of the infinite fountain of God's love for us and others.

This is a life-long process and the essence of our spiritual maturity i.e. our day-to-day sanctification.

²God, our neighbor, and other brothers and sisters in Christ.

The closer and harder we look the more of his love we discover.

³Self affirming activities are endless. It’s simply any activity we engage in to make ourselves feel good. This can be done through drugs, sex, achievement, entertainment, recreation; being better or different from others to make ourselves stand out - i.e. look more significant than others to gain praise and on we can go. Fill in the blank. It’s important to understand none of these things in themselves are necessarily wrong or bad. All things are created by God for His glory and our joy when used properly. Why - to what end - we seek them is the problem.

⁴This does not mean we find no joy in helping others, but that joy is in the others' joy, not in the joy itself.