If there are three switches for a single light two are 3-way and one is a 4-way switch. The numbers refer to the number of screw terminals on the switch (believe it or not)3 screw for a 3-way and 4 screws for a 4-way (not including any ground screw). You can replace ONE of the 3-way switches with a 3-way dimmer.

Hire an electrician. Taping wires together is not safe or legal. It's impossible to tell with the limited information here, but you'll need to take apart the switch at the other end to be sure. I suspect the three wire is part of a 3-way switching. Two of those wires go to the other switch and the third, along with the remaining wire from the three wire go to the light. The white wire from the light should connect to the white wire going to the source (and preferably through the white wire in the 3-wire cable, although this sounds like it has been screwed up already). If the two reds are the alternate sides of a dimmer that supports 3-way circuits (read the instructions) then they to each of the two wires that go to the other switch.

You need to run a cable from the existing fixture box to the new location of the switch. You don't even need to change the fixture if you leave the fixture switch always on. The wiring will look like this. http://www.selfhelpandmore.com/switchoutlet/basiclightswitch/basiiclightswitchsl.htm

We bought our 1964 house last year with its original electrical. When we moved in, we replaced all of the old switches with decoras and dimmers, and we replaced the outlets (which were all 2-prong) with grounded 3-prong. When we redo the kitchen, we plan to upgrade the circuit box to a 200 amp (or possibly larger to leave room for later additions). To be honest, we did not realize that the outlets were all 2-prong, but we would not have let that deter us, since we had a fairly specific wish list. Things like outlets/outlet covers are simple to replace as long as the electrical is in otherwise good condition. The things that would have been deal breakers for us were: old asbestos duct work; asbestos cottage cheese stuff on the ceiling; no a/c original pipes roof in need of replacement too much wallpaper throughout the house (I HATE stripping wallpaper) Signs that the house had been neglected Things we didn't really care about: Needing new paint or carpet/decorating issues An old kitchen or bathrooms, as long as they were in working order The old electrical outlets and switches Things that I wanted to change, but which were relatively simple to fix