Once you get good, you can just paddle upstream to get back to your car. You'll see a lot of people that look like they are "playing" in holes and waves in the middle of the river; they are actually trying to be like salmon and get upstream to their vehicle. You'll eventually be able to recognize this activity for what it is, but until then...
Generally, since you NEVER KAYAK ALONE, between you and your buddy or buddies, you'll have two vehicles. Park one at the take-out with all your dry clothes, then head to the put-in in the second vehicle. There are, of course, many variations to this. For short runs, say less than 2 miles that have a creek/riverside trail or road, you can park at either bottom or top and walk either before or after your run. If the run is further, say a few miles, you can do the same but with a bike. Typically in this situation you drop all gear and buddies off at the put-in, then drive to the take-out, park the car, then ride a bike to the put-in.
In some situations there are companies that will shuttle your vehicle(s) for you. This is typically only on multiday runs through remote areas. For example, Gates of Lodore in Colorado/Utah is typically three days and 45 miles on the river. That wouldn't be too bad of a shuttle (90 miles out and back) if a road followed the river, but there is no direct route. In reality, the shuttle is an 8-hour drive. Thus, some of us pay a shuttle service to take all of our vehicles from the put-in down to the take-out.
There are many whitewater clubs out there, and they are a great way to get into the sport. Once you get to TN go to a local boat shop and ask about local clubs. It's even possible your school will have one. Oftentimes clubs can help with low-cost gear, usually help with learning skills (like rolling during pool sessions), and are always a good way to meet other boaters.
As for boats, do a search. It seems that question is asked at least 15 times per week.
Finally, though there are people from all over the world here on MountainBuzz, we are mostly a Rocky Mountain region forum. BoaterTalk.com seems to focus more on the eastern part of the country, and may be more useful for you to hook-up with other boaters in that area.
Welcome to the sport, be safe, and have a blast!
"A witty saying proves nothing."
- Voltaire (1694-1778)