When the strings start to unravel. <--- Obviously - lol

When they become less vibrant, which is hard to tell when the decline is spread over time.

When your fingered fifths are off.

E strings can be changed quite often. I usually change them after 8 weeks if I play a lot.

Different types of strings last longer or shorter depending on their materials but you can expect good quality for about 3 to 6 months and perhaps as much as a year if the instrument gets very little use. That being said, one can continue to use the strings past their optimal period, though changing them will improve responsiveness, action, power and quality.