I am not an expert at computer analysis or any analysis. However if you have the time, I found that the best way to use computer analysis is to go through two stages. First stage, I analyze the game without computers, just looking at where I think I went wrong, and trying alternative moves/lines which I myself figured would be corrections to my mistakes. Then I would fire up the computer and let an engine like chessmaster or shredder analyze the game. I would compare my analysis or suggested moves to the moves suggested by chessmaster. Often I would find out that chessmaster finds new moves to improve on the mistakes I made. Sometimes the reason for the move is quite deep and you can use the engine to play through alternative variations of those moves until you understand why those moves are correct for chessmaster. But there are a few times that I disagree with chessmaster and find my moves to turn out to be just as good, especially in positional situations. You can use the chessmaster engine or other engine to play through the variations of moves you suggested just to make sure you didn't make a mistake or overlook something in your variation. Gary Kasparov said that he used fritz to check out his analysis. Which means he analyzed first and then used the engine to make sure his analysis was sound.
How to use chessmaster analysis

Chessmaster isn't the best tool for analysis, I'd recommend Arena + Rybka 2 which are both free (google them).
However, a numerical evaluation and a sequence of moves are what you're going to get, whether you'll analyze it with chessmaster or not. You know what those numbers mean, right, for example 0.90-/+ mean Black has an advantage (.90ths of a pawn), while 2.30 +- mean white has decisive advantage.
You should understand that the variations are not random. They tell you what the engine thinks is the best continuation.
How does one learn from the chessmaster analysis? Most of the time, my moves only change in score by +-.1 with a random sequence of moves afterwards...not the most helpful thing.