I am notsure how they are started in USa as I am in Canada but I trained my 3 yr old TWH mare start to finish thus far, however I have had a 30+ year experienced trainer and shower on the ground with me to guide me (which gave me a lot of solid knowledge, but still i'm not years and years of experience). I can tell you if you have a typical minded TWH you'll find your horse very willing to learn and intelligent.
I think the starting portion of a TWH is fairly similar to any horse, leg aides, turns, bends, giving to the rein, whoa (haha) desensitizing, etc...once they are able to walk around an arena under saddle is when you can start with the finishing and gait training, collection, etc... to start with, at least for us, we just focus on getting them ussed to a saddle, a bit, legs on them and all the basic things any broke horse should know how to do.
Here is my 3 yr old mare Sable (the pally), she is 3 and barefoot...the black mare is Bloom another horse I show with. Both aer very competitive show horses and have strong american bloodlines. So this is essentially the look you aim towards. Hope you post more info as you go along!!