How long should I wait before exercising the same muscle?

When you workout a muscle, what you're doing is damaging the muscle in hopes that when it heals, it'll heal stronger. It isn't until you rest that the repairing begins.

If you're constantly exercising the same muscle, chances are it won't have enough time to rebuild itself. You're doing more harm than good. At the very minimum, you should wait between 48 and 72 hours (2-3 days) before working the same muscle twice.

Most exercise routines will not have you working out a muscle more than 2-3 days apart (especially at the beginning).

You can realize a lot of benefits by working out a muscle once per week or you can use the ACSM guidelines and do a full body workout 2 or 3 times a week.