Competition license typically you have to have a reace prepped car or else rent one. Go to two SCCA road race driving schools and pass them successfully then you can run two races as a novice with novice permit. You have to complete those two races with what is considered passing grades, then you can race in regional races. You have to complete a number of regional races (forget how many, but about 6) then you get your National Competition license. This lets you race in any SCCA club road race. You have to run a minimum of 4 (I think) races each year to keep your license current.

Expenses:
Car: ~$5,000-$200,000
Personal equipment ~$1000
(driving suit, physical, etc)
School entry fee: ~$400
School expensees: ~$500

6 Regional races entry: ~$800
6 Regional race expense: ~$1500

Those are ball park minimums.