When playing in a tournament, it is generally not possible to analyse one's games immediately afterward. There simply isn't time. Still, it should be done just after the tournament, when you might still be able to remember what you were thinking. "Well, I considered Bxb5 here, but did not like ...Qe5+. Now I see I could have played...." You get the idea.
Do not use a computer.
I cannot stress that enough. You will not learn to look for better moves, and you will not look for your mistakes. You will just let the computer do all the work for you, and you will learn nothing. Only after you have done a thorough analysis yourself should you submit the game to the computer. And put your analysis in, too, to see whether you missed moves in your analysis.
Classify the moves you missed. When one is a novice, they will be simple things such as hanging pieces and missed checks. Then they will move to missed forks, undefended (vulnerable) pieces, and things of that sort. At advanced levels, it will be moves that influence center control, piece mobility, and pawn structure. And it may just be the loss of a tempo that is the difference between a win (or loss) and a draw. Finding such mistakes is, of course, more difficult. When you have a bunch of those, see what types of moves you are most likely to miss, and look for them in future games.
Get a coach
If you can, get a coach to review your analysis. He may or may not be of any more use than the computer, but he will provide accountability.