This passage goes hand-in-hand with Proverbs 3:6 where we read, "...and He shall direct your paths." It is one of those thoughts that many Christians have had over the years, "the Lord has a plan for my life." We believe that as we surrender our will to Him, He directs the way we should go. Sometimes, He clearly gives us a burden to go someplace and do something that we feel we must obey. Many missionaries and pastors had that kind experience. They will say, "The Lord spoke to me" or, "I was led by the Lord..." These are certainly Biblical patterns, most noteworthy is the call of Paul and his companions to go into Macedonia and "help us" Acts 16:9.
Then, there are the times when the circumstances of life are so ordered by the Lord that one finds themselves doing God's will before they realize it. A clear example of that is Joseph's being sold into Egypt. Certainly not his desire, but "God meant it for good" Genesis 50:20. This is not always easy to see until the whole picture is revealed and you realize God "led me all the way."
The latter part of this verse is translated here as God being the One who delights in the way of His obedient children. However, the New International Version presents this verse as, "The Lord makes firm the steps of the one who delights in Him." This gives the thought that as a Christian is led by the Lord he will find himself delighting in the way God has moved in his life. That certainly isn't true at first, as in the case of Joseph, but eventually the believer who follows God's way without disobeying, will come to a place where they see "His way is perfect" Psalm 18:30.
Trust the Lord and don't try to lean on your own thinking - He will order your steps. And you will be pleased.