How long does a contact lens generally last?

Depends. Each lens is designed to last a different amount of time. Some lenses are replaced daily, some two weeks, and some one month. A few lenses are replaced quarterly but these need to be enzyme cleaned weekly. The difference in lenses is how well they repel protein and other deposits.
It varies a lot. Different lenses are designed to be worn only once to annual replacement cycles. Most disposable lenses are worn 2-4 weeks before replacement. This is determined primarily by what the lenses are made out of. Best to stick to the recommended replacement times.