You want to do actual Club Racing? What car are you going to use?
It takes a while to get a full race license. To get started, you should locate your local SCCA region by clicking on the "find your region" button at scca.com, then when you find the local region, check their schedule and join their forum. You'll have to do some autocrosses and some PDX track events to get experience, then work your way up to racing. You'll need to pick a series to run in and get a car for that series and be sure it's fully race prepped with a cage, fire extinguisher, window net, and everything else. Read their rules to be sure...
There is some misinformation being flung around here. Hopefully I can clear it up, maybe if you read my thread you can see where I am coming from.
To do SCCA auto-x you do NOT need to be 18, just have a valid drivers license.
To do club racing...you usually have to be 18 some clubs you have to be 21. There are different forms of club racing, the ones I am familiar with are Bonnet and Boot, Shelby Club, CART, SCDA, PDA and such. They require you to be 18 and have a drivers license.
Now when you want to start getting into sanctioned races i.e. SCCA regional races (I'll speak on SCCA as I don't know NASA all that well) you will need to have ATLEAST a novice permit. The quickest way to get one is to attend a racing school. Skip Barber offers a 3 day race school where you attain your Skip Barber Novice Permit and and once you complete the necessary paperwork this will be your Regional license. Then you can do the 2 day Advance Driving School or 2 lapping sessions and be signed off for your national license.
Once you do that and you want to start racing, find out what class your car will fall under and start preparing it safety wise for that class. There's nothing worse than showing up at an event to race but to be rejected because you didn't install the proper safety net or seat belt or seat.
So for some level racing you do not need a full license or license at all. I recommend you do a track day. Whatever track is local to you, get their club schedule. Find a club that you can run with. Generally Porsche clubs don't like other cars running with them, but they will if they are not full. Find a club where they will have a wide variety of cars. There will be minimal safety requirements and you can get an instructor to ride with you for free.