How do you get your faith to become stronger than your feelings?

Faith is not emotions or feelings. Faith is knowledge of the truth. In other words, if the Bible says, "God is near you" (Eph.2:13), then faith believes that, irrespective of emotions and feelings. If your emotions rule you, then your life will be like a roller coaster, constantly tossed between the highs and the lows. Emotions cannot provide you any stability in your relationship with God. However, if you stand on faith, then no matter what your emotional state, you have a firm grounding, and God will be near, because truth says so, not because you think you feel Him.

How do you learn to have faith? Well, remember that your whole being, your flesh (or human reasoning), defaults to emotions and feelings. Your default response to everything is feelings since you are conditioned on these since you were born. But faith comes by the Word. You grow in faith by learning the Word, studying the Word, gaining knowledge in the Word. As the Word starts to fill your thoughts, you will start to respond to that knowledge, because of faith, and in spite of your feelings.

I'm not saying that you must become a robot (android) without feelings! No. Feelings and emotions will always be a part of you. Emotions are good, they give you personality, they shape your responses, they make you happy, caring, and loving, but they also have the negative side, and can make you angry, give you frustration, or bring you into despondency, etc. Nevertheless, although you have emotions, you must not let them rule you when it comes to your relationship with God and with truth. Emotions must never be allowed to lie to you, saying that God is far away, when you know the Word says He is near. Truth must triumph over feelings. Emotions must come in line with truth. Another way to describe it is that Satan can mess with your emotions, throwing arrows of negative thoughts into your mind, but he can never mess with the truth. 

The Word tells us that the Christian walk is one of faith, (Rom 1:17, The just shall live by faith). It is a tricky thing to try and live the Christian life when it's ruled by your emotions. Paul, our pattern and example in Christ, says in Phil.4:11-12, that he was content, whether he was brought low, or when he abounded. He learned the secret of being content whether he had plenty or whether he was hungry, whether he was in abundance or when he had need. This is possible only when your faith in the truth grounds you. You are able to stand on a sure and stable foundation no matter the circumstances which would typically plague the emotions.

What was Paul's secret? How can you learn faith like he had? It comes by getting the source of faith into you. The Word must become part of you, part of your constant thoughts, part of your soul. One sure way of getting faith to become stronger than your feelings is to read the Word as often as you can. Read it, study it, sing it, meditate on it, dream of it. The more of Gods Word is in you, the more faith becomes strong within you.  

Phil.4:8 Finally, my brothers, whatever things are true, whatever things are honest, whatever things are right, whatever things are pure, whatever things are lovely, whatever things are of good report; if there is any virtue and if there is any praise, think on these things.

Col.3:16 Let the Word of Christ dwell in you richly in all wisdom, teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord.