My advice to you is to start drinking heavily.
A lot of good advice above, but there's a political aspect to this which is very important.
How you do will very much depend on the expectations that management has. They very often assume maintaining code is much easier than writing it in the first place which is of course the exact opposite of the reality. Make sure you talk with them about expectations up front, about how soon they expect you to be competent in the code.
In all honesty, I worked somewhere that had inherited about 800,000 lines of code, with 5 very sharp guys, and no one understood the code even remotely close to the original authors after 2 years of supporting it.
Companies need to understand that unless they pair program, when they lose the programmer, and he didn't have a partner, they lose the code. You might as well just rewrite it because it will take a new person as long to understand the old stuff, longer perhaps because he is not learning it in the orderly progression that was there when it was written.
There's a maxim, "He whose work is the most incomprehensible gets the most respect". The suits and pin heads who run software companies fall for this 100% so the worst programmers, who by luck of the draw got to write the first spaghetti mess, are glorified while the maintenance programmers are seen as little more than janitors.
I make it a rule to go on unemployment before accepting a job as a maintenance programmer. Avoid it at almost any cost! It's a thankless job that usually ends in frustration and tears unless you have a VERY understanding manager or circumstances have granted you a very successful product that needs few fixes or enhancements.
Often companies hire programmers when they are behind or they lose people because they overworked them. Thus you are coming into a bad situation, already behind with everyone expecting miracles.