2001 chevy cavalier starts when it wants to?

Starter solenoid may be going out. Have it checked. Pull the starter and take it to a shop for testing. Most starters come with one attached to the starter, but you can buy one and attach it yourself. Check the teeth for excessive wear also.

Check your battery cables at the battery for corrosion, make sure they are clean and tight. If you just get a click, click, click, sounds like battery connection.