David inquired of the LORD, and the LORD answered him, "Go down to Keilah, for I am going to give the Philistines into your hand." -1 Samuel 23:3-5
"David inquired of the LORD, "Shall I pursue this raiding party? Will I overtake them?" "Pursue them," he answered. "You will certainly overtake them and succeed in the rescue." -1 Samuel 30:8
"David inquired of the LORD, and he answered, "Do not go straight up, but circle around behind them and attack them in front of the balsam trees." -2 Samuel 5:23
David's life is such a great example of a man seeking after God and yet at times really messing things up. At various points during his life we see him "inquiring of the Lord." This is coupled with resulting wisdom and success in his endeavors. At other times, he did not "inquire of the Lord" and reaped negative consequences such as a broken family, adultery, murder, and a plague upon the nation of Israel.
I think his life can very easily be applied to most people today. How often are decisions made without inquiring of the Lord? While sometimes things work out fine, at others the Lord could have provided insight and wisdom into the situation that would have resulted in greater success or avoided poor decisions and heartache. In my own life, I sometimes do well at inquiring of the Lord and seeking His wisdom. It is at these times that I most sense His presence and guidance in my life. At other times, I do not inquire of the Lord and rely on my own understanding and capabilities. Inevitably, mistakes or awkward situations occur that could have been otherwise avoided.
I Thessalonians 5:17 says "pray continually." This fits nicely into inquiring of the Lord. When we are continually in a state of prayer, we inquire of the Lord and have His constant guidance. It is definitely something that takes practice to become skilled at. Next time you're driving in the car, exercising, shopping at the store, or doing other daily tasks, visualize Jesus presence there with you and talk with Him. By building a constant relationship, you can much more easily hear His prompting and feel comfortable inquiring of the Lord.
A really good short book written by a 17th century monk that covers this concept very well is called The Practice of the Presence of God by Brother Lawrence. He writes about learning to experience and know God's presence even in regular tasks like cooking or washing dishes rather than only in dedicated "sacred" times.