Changed my guitar strings last night whilst watching the old folks documentary.
Stringed instrument players have different views on how often this activity should happen. There are some who install new strings for every gig; some who are still playing on the set that came with the guitar when they got it five years ago.
A lot depends on how often you play, how toxic your skin oils and perspiration are, and how much maintenance you do -- wiping the strings before and after every playing session with a clean cloth, or using some of the string-cleaners made for that, all make a difference.
Even the best strings for guitars aren't that expensive, though in a pinch, you can boil the old ones, dry 'em off, and put them back on, if you are careful.
I tend to fall into the every six months or so category. The basses start to corrode, especially just above the frets. The trebles get stretched out, and they all go out of tune more often. The guitar seemed to lose its punch, has less resonance, seems kind of dead. When that happens, I have to change the strings.
New strings take a while to settle in. As they stretch and set, they will tend to go flat fairly quickly. Tune up, play a few chords, they are all out-of-tune. There are a couple ways to get around this: Play a long session and keep tuning until they start holding notes. When you are ready to quit, tune them all a bit sharp when you put the guitar away. And just accept that for the next few sessions, you'll spend more time turning the pegs.
Then, for a few months, the guitar sounds pretty good. Well. At least as good as I can manage.
The right strings, by the by, can make a so-so instrument sound much better. Of course, there are whole religions based around which strings are the best, but this tends to vary from instrument to instrument. One guitar will sound boffo with Brand-X, another instrument just like it from the same maker won't care for those at all. You have to find the ones your axe likes.
For the classical players out there, if you haven't tried them, you might want to risk a set of Aquila's Alabastro -- I use the normal tension -- and they give my guitar a warm, woody, gut-string tone. Their trebles are what they call Nylgut, and while they are a little spendy, they are way cheaper than real gut strings.