Well, it depends. On what?
The hard limit is when the string breaks. When a string is broken, it needs replacing. This much is obvious. It's the rest where it gets difficult.
Lots of players like the bright sound of new strings, before finger oils and persperation pH issues deaden them. Al diMeola is the most intense I've heard of on this, switching strings between takes of a song. Most touring acts change strings before each gig. On the other hand, lots of jazz players play roundwound strings, which sound less bright and more "dead" out of the bag, and even without them, some folks leave their strings on forever. James Jamerson, the bassist for every Motown song you ever cared to dance to, changed strings only when they broke.
The "happy medium" is a few months, depending on how much you play. I swapped in a set of Slinkys for my lap steel (big mistake, you want heavy strings for a lap steel) after six years or so. My banger, which has a truss rod popping out the neck, has had the same set of Elixirs for four years or so. (Elixirs have teflon-coated strings, which mitigate the pH and oils probles and stay "bright" longer, but they have less of the bright because of the coating. I recomend you go for Elixirs when you decide to swap 'em.)
Beyond tone (which you might not be experienced enough to hear differences in yet), look for your strings showing wear and bent points at the frets. I used to get the windings of my G string unwound, but I was playing with a brass pick. With brass picks, you get the tone of a light pick but it won't bend, so it feels like a medium or heavier. Thing is, they eventually get like you're playing with a knife edge and your cutting into your strings. They're OKish for electric work, especially playing leads, but if you're trying to play acoustic in an electric band, you'll be carving into the windings.
And dude, if you have any questions on anything guitar, just ask, OK?