What is awakening/enlightenment? It is the destruction of the false belief that you are a thinking, experiencing, doing person. When this happens, you live in your true nature, which is inexpressible, perfect, stainless, and unchanging. Actually, these last couple of sentences are not quite accurate, since the real truth is beyond words, but they are accurate enough.
If you have a strong, unconflicted desire to awaken, the steps are very simple.
Self-inquiry means trying to locate the self-evident knowledge that you have that "I am," (that is, the source of awareness) and not accepting any particular sensation, thought, or feeling as it -- because the "I am" is aware of all these things. Simply focus on trying to find the real I am at all times. How do you do that? Every time you think the word "I," a bell chimes somewhere. Follow, as best you can, the sound of that bell. If you think you've found it, you haven't. Keep looking until there is clarity. If you have to ask whether there is clarity, there isn't.
Ignoring all thought (also known as surrender) is exactly what it sounds like. It's the simplest way of all. It's not about stopping or fighting thought. It's about moving your attention away from it. The TV could be on, but you could refuse to pay attention. Refuse to pay attention to thought. All thought. Repeat till clarity.
Either self-inquire or ignore all thought every waking moment. If you "lose it," come back to it. Keep doing that until there is clarity. If you do it intensely, clarity will come. Again, if you have to ask whether there is clarity, there isn't.
That is all it takes to awaken. Though the steps are simple, the mind can be tricky in response to these instructions. A teacher can be very helpful for guiding you through this process and keeping you on track.
Now if you do not have an unconflicted desire to awaken (most people don't! -- this will become apparent if you have low motivation to do the above practices, or you keep getting seriously distracted by various other things), you can strengthen it by getting an intellectual framework around the awakening process (through asking questions of a teacher, scriptures, etc.) and by dealing with your emotional baggage (this comes to being more honest about what you want -- psychoanalytic psychotherapy and artistic expression of your feelings can be very helpful).