Is there a majority opinion as to what giving up free will and giving it to Jesus means? What does this action look like? Are there any real life examples?
I hope that I can help here.
A couple months ago I got engaged. I prayed a lot about the decision and felt like it was a good move in my life. One that would be hard but would be worth it. Well, 2 weeks ago my fiancee broke up with me. That was one of the hardest days of my life. And it would of been so easy to say, "I prayed; it felt like a good choice, I was doing everything right, why did God allow this to happen?"
I could have blamed God and Jesus for all the pain I felt. Instead because of experiences I have had in the past I turned to Jesus and God and relied upon their love and grace. I have in the last two weeks learned more about my relationship with my Savior then I think I have in the rest of my life. I still hurt, true, but I have comfort in the knowledge that my Savior and my Heavenly Father love me and have a plan for me that will lead to even more happiness then I had with my fiancee.
So to me turning your will over to the Savior means trusting Him in those hardest parts of your life. Knowing that it will strengthen you and that Christ has other plans for you.
Scripture reference was asked for so here goes:
Applying this to my story above. I could have ignored Christ and tried anything and everything to get my fiancee back. That may or may not of worked but I would not of drawn as close to my Savior as I have in the last couple weeks.
I'd like to add some scripture that I think goes along with the scripture @ryanOptini quoted, and will also help answer your question.
(I quoted the Amplified translation because I like its extra notations.) This is the concept of "surrender", which is vital in letting God take the reins of your life. Many Christians fail to take their faith to the next level. There are sins that we hold onto and don't give to God. We can even reason within ourselves as to why these things might be acceptable in God's eyes. Either way, we take what we want and leave what we don't want. You might hear preacher's call this salad-barring God, or keeping your pet sin's in the closet. Anyway, in this passage, Paul urges us to offer our bodies as a living sacrifice, holy and pleasing to God, as our proper service and worship, so that we can have a renewing of our minds (and be transformed by it), and fulfill and prove the good and perfect will of God in our own lives.
The keyword in most translations is offer, and as Amplified puts it: A "decisive dedication". This is not as hard as you, or at least I, would have thought it to be, as I always thought that I could not fully live for God, because it is way too hard.. and it is just too much to ask (I don't have the willpower). But all it is is simply making a declarative decision to no longer live for yourself, or anyone/anything else, but God (through which of course you will live for the interest of others also)! God's Spirit will then do miraculous work within you to cleanse you of your "pet sins". In your offering, you will be convicted, you will weep, and you will repent; and this will be a continuous struggle for some things as you will not be made perfect. You will still be tempted, and you will still fall; but the key is to not give up and become numb to it, but pray for conviction of the Holy Spirit, that you may have repentance and be reconciled to God in His mercy. Without this, the bearing of your cross, the surrender, or yielding, to God and the Holy Spirit, we cannot be proper disciples of Jesus, and thus the Light upon us and our path becomes darkened.
Sorry if my answer is incomplete to your question. I hope this helps in some way. A great lesson is taught on this subject by Chip Ingram in his R12 study.