I went back to read the scripture you quoted. That is a good passage, especially if you read the whole thing. I quote Galatians 5:22-23 a lot because it shows us the fruit of the Spirit.
I will give you a small synopsis of how it has shown itself in my life.
Just today I was considering if I wanted to do this job for a friend of mine. Pondering within myself if I actually had to do it because it was asked of me (which scriptures tell us we should). But my own flesh didnt really want to do it. Well she came to my door today and asked me how much I would want for doing it. And what my own will wanted wasnt even a thought in my head. I was agreeing to do this for her, at whatever she wanted to pay me.
Which was totally opposite of what was just going thru my noggin earlier, lol. So the Spirit within me was directing me how I should be. And without realizing it, I was submitting to the authority of God, thru his Holy Spirit.
This is explained by Paul in the Galatians you are looking at. When the Spirit controls our lives, he will produce this kind of fruit in us: love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, and self-control. Here there is no conflict with the law.
This is walking with the Holy Spirit. (Not following our sinful desires, but following what the Spirit of our Lord has for our lives).
The gospel of John speaks of this Holy Spirit: When the Spirit of Truth comes he will guide you into all truth. He will not be presenting his own ideas; he will be telling you what he has heard. He will tell you about the future. He will bring me glory by revealing to you whatever he recieves from me. All that the Father has is mine; this is what I mean when I say that the Spirit will reveal to you whatever he recieves from me.
Jesus said this: My prayer for all of them is that they will be one, just as you and I are one, Father- that just as you are in me and I am in you, so they will be in us, and the world will believe you sent me. I have given them the glory you gave me, so that they may be one, as we are- I in them and you in me, all being perfected into one.
So walking in the Spirit of our Lord, is us being one with him. Denying ourselves, and following him (and his will).
Living our lives everyday, with the Holy Spirit of our Lord revealing to us the way of truth; and guiding us on the path of righteousness for his names sake.
God Bless