Most manufacturers recommend changing your stylus at around 1000 hours of record playing time. So if you’re using your turntable for an hour or so per day on average, ideally you should be changing the stylus every couple of years. This varies depending on the manufacturer and what type of materials they’re using. It’s worth checking the manufacturer's recommended lifespan for your stylus when you get it. Some hi-fi fans will say sticking strictly to the manufacturer lifespan is being overly cautious (as long as you're cleaning the stylus correctly and playing well-maintained records in decent condition), while others say replacing your stylus within its lifespan is essential to preserving your records and getting the most out of your set up. It's your call how daring you're feeling.
Ultimately, it’s not an exact science, and there are several factors that will affect the rate your stylus will wear.
Depending on the cartridge you're using, you may be able to replace just the stylus, or you may need to spring for a whole cartridge. Most moving magnet cartridge's offer replacement styli, which you can usually just clip into the front end of the cart. Often you can even sub in a more expensive model for a performance boost. If you're using a moving coil cart, a worn stylus usually spells the end, though the manufacturer may offer retipping.
There are a few things you can do to treat your stylus right and prolong its lifespan (if you're brave enough to flout the manufacturers recommendations). The most important thing is to treat your stylus with care, keep in mind how many hours it's in service (ballpark is fine), and ensure the records you're playing are clean and kept in good condition. In the end, hours of playback means your stylus is going to wear out. Make sure you replace it before it starts doing damage to your records.