My interpretation of faith in regards to this scriptures and my experiences is not an easy task, but I will try to explain.
Faith believes in ability that does not come by natural means. This ability is divine and can only be given by God. The bible says that God has given to every man the measure of faith. This may seem like a double standard, but it is not. Yes mankind has the ability to believe in something or someone. However, although this faith that man has is powerful, it is limited. This faith is limited by his condition. For example, Michael Jordon often spoke about how he believed in himself to be the best basketball player. He worked at it, and would not give up. This type of faith is great. Yet if Michael broke both his knees  he would be limited by his injury  no matter how hard he tried,.
The faith that I have, reaches far beyond man's power. I am talking about faith in God and the words he has spoken. Faith is not denominational but rather it is relational. When I put my trust (faith) in the Lord Jesus Christ, I was given divine ability to experience the true and living God. That is how I came in contact and then communion with Him. The bible says without faith it is impossible to please God (Hebrews 11:6). I just did not put my trust in things or people that are limited, but I put my trust and dedication to one who loves us and has all power. Since then I have received joy, peace, ability to love the unlovely, integrity, and great incite into myself and others. I am not saying I am perfect, or am better than anyone else. I do not judge others based on their beliefs or practices. I believe that God loves everyone. He may not agree and accept everyone's condition, be he does love everyone. He loves us so much that he gave us a way out of our sinful and unhappy condition. He sent his son Jesus Christ. I know it seems that I am speaking about doctrine but I am not. If denominations and other religions had no name, then one could see the faith that I am talking about as a way (answer) out rather then a person or certain sect.
I can only speak from personal experience and not practices that come from compromising traditions. I love the Lord Jesus Christ. He has given his life for me, and I have given up my life to him. My life that I live, I live by the faith of the son of God who loved me and gave himself for me (Galatians 2:20).
Don't worry I do not go around beating people over the head with the bible. I have learned to be the bible. That means, what God has said and done for me can be seen through my Character, and my love and commitment towards others.

God bless you!