My Second Dragoon uses #10 Remington caps, which is surprising, as many of the online websites that sell it recommend #11s, which fall off unless you pinch them. As was mentioned, loose caps are the #1 cause of chainfires. If in doubt, buy one of each, or find someone who might have some and see if the 10 will fit. If it does, use it.
My Dragoon likes the .454 RB, but some have been known to eat .457s. You want it to be a tight enough fit that you shave a tiny ring of lead as the ball seats, but you shouldn't have to push so hard you'd give yourself a hernia. Again, I'd recommend the .454s to start, and if they seem too loose, use the .457s. Powder; you can use real black, or Pyrodex (my choice as it is non-progressive fouling, which means you won't have fouling building up to the point where things don't rotate after 50+ shots. I would start off with around 40 grains as a starting point, although the Walker will hold up to 60 grains. With charges above 45 grains, you may start dropping your loading lever due to recoil, which will freak you out 'cause the cylinder won't rotate with the ram stuck in a cylinder bore....if it does, just lift it up and carry on.
I'm surprised nobody mentioned Wonder Wads....simply insert a WW over the powder, seat it with the loading lever, then seat the ball. You can then skip the messy ol' Crisco or Bore Butter (unless you're using real black; it will help soften the fouling but it makes a hell of a mess IMHO). Powder, Wad, Ball in all six and you're ready to cap at the line. I don't recommend loading all six if you're not at the range, keep the hammer on the empty chamber and load five.
Colts tend to swallow caps, so after each shot it's a good idea to lift the muzzle and tilt it to the right; most time the cap frags will drop right out. If you do swallow a cap, don't freak. Pull the barrel and cylinder, cock the hammer, and in most cases you can dig it out with the pocketknife you're gonna remember to bring 'cuz the Cap'n told ya to.
I strongly recommend getting a good set of GUNSMITHING (not Craftsman or Home Depot) screwdrivers (these are specially ground to fit gun screws without boogering them up....which you didn't do yet...did you?) and disassembling the gun. Why? Because you're gonna need to disassemble it to clean it, and it's much easier to take it apart and learn how it all works NOW when it's clean, and you haven't been out shooting all day and you're tired, etc...and not when you're trying to clean it at the same time. This way, if you eat a cap at the range, you can decide whether or not you want to really delve into it there, or call it a day, knowing how it works and what's inside it.
I would echo everyone else's recommendations on the degreasing and cleaning. I lube the cylinder teeth and arbor with white lithium grease and use Rem Oil on the outside of the gun. Most folks clean up with soap and water but I prefer Hoppes #9 Plus Black Powder Cleaner and patch lube. Face it; water+steel=rust. You pays your money and you takes your chance. You will also need a nipple wrench (one that fits the Walker)...Traditions nipple wrenches have a handy nipple pick in the handle...and when you clean the nipples, put a little dab of anti-seize on the threads. You'll thank me later. (You're welcome). A standard pistol cleaning kit in .44 cal will work, but get a toothbrush as well.
Here is a link for a parts breakdown on the Walker:
http://www.coltparts.com/pt_walker.html
If you get stuck or have any other questions, please don't hesitate to PM me. I'll help any way I can.
FYI- here are a couple of You Tube links to give you an idea of what it's all about:
http://www.youtube.com/watch?v=fPMr8ix3aZ0
http://www.youtube.com/watch?v=B2N6FoKB4a0
http://www.youtube.com/watch?v=LDPa-539JQ0
Enjoy it!