Many people are not really sure what self-inquiry is all about, but it is also known as meditation, which is more well known. When meditating, you access deeper brainwave states. This is accomplished by clearing distracting thoughts, reducing stress, and sharpening your thinking. Meditation helps you get your emotions under control as well.
The best way to get in tune with yourself is to get comfortable. Get into a nice chair or sit on the floor. Your comfort is paramount in getting in a relatively calm position and letting your mind relax.