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What's the best way to clean a trumpet without ruining it?

I suggest you follow the instructions on this page.
I feel it is very complete and accurate, and it is the method I personally use. Just make sure the water isn't two hot. I read somewhere that can cause the finish to come off eek

I also read somewhere else it is suggested to wash your trumpet every 3-4 months. However, I usually only wash mine every 6 months. It's all a matter of how dirty your horn is and how often you play it. I'm not a expert, so I would also suggest doing some research or talking to an actually expert.

Take you valves out, set them aside. Don't forget what order they're in. Take out all of your slides and set them out. Take the metal caps off the bottom of your valve casings. Put a few inches of lukewarm soapy water in your tub (its best to use dish detergent, cuts the grease). Put everything in but the valves. Let soak for a little bit and then wash it with a wash cloth and use a snake to snake out everything. Rinse it off, dry it. Put everything back together and regrease/reoil.

*You can clean the valves by using a q-tip and some warm water. Just don't get the felt wet.

Is it silver, brass, or something else?

If it's silver, then you need to polish it afterwards. Use Wright's Silver Cream (my band finds it to be the best)

If it's brass, just buff it with a clean cotton cloth afterwards to help make it shinyer.

If something else, follow the instructions for brass.

because the trumpet is a thicker, and defiantly more durable piece of metal... the valves tend to bend or get dents in them much easier...plus they cost much more to get fixed because each 'hole' is cut in particular dimensions...