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.

It is usually best to use a meter to test which wires do what, otherwise, you may be going back to the store to get another dimmer. There are several ways to wire a 3-way, so there is a chance that you can't tell by looking. It sounds like yours are wired like this diagram. The different color terminal is called the "common". The other two matching colored terminals are the travelers. Notice that the two traveler wires come out of the same cable, and the common comes out of a different cable. As long as you get the "common" in the correct place, the other two travelers are interchangable regardless of color. One traveler should be a red wire and the other one a black wire. The common should be a black wire.

That didn't go quite as smoothly as I'd been led to believe but in the end I have all (7 not 8) switches being sent to me. I've had about 6 people tell me all I needed to do was get the model number from the switches and let them know which ones I needed. I was also told that the model that works with CL and LED would be the replacement. My brother pulled the light switches. You don't have take them totally out of the wall. I called Lutron with the model numbers and was told they needed the date code too. It's in a different location and not visible in the pictures I took. That's the first I've heard of that! We already had the switches back in and covers reattached. That was a bit of an argument but the tech finally agreed that they didn't have to have the date code. Then I mentioned that I'd been told the replacements would be CL and LED compatible. "No, they will be like for like" :o Another minor argument with me suggesting they listen to the previous recorded conversations. OK, they're sending the CL models. BUT, CL model doesn't come in a 1000w version. I ask what am I going to do since incandescent bulbs have gone the way of the coo-coo bird. I have to buy new recessed lighting? Tech says "you can still buy incandescent bulbs. They aren't going to stop making them". Now I'm confused. I've heard for 1`0 years they are being phased out. Wasn't that completed last Dec? I stocked up on light bulbs so I haven't even looked in the last several months. He said manufacturers have to make incandescents that (for example 100w bulbs) only use 72w for a 100w of light. Now I'm really confused. I have no other option but to order the MA-1000 like I have since they don't make it in a CFL compatible. Does anyone know if this is true? Are incandescent light bulbs still being made but they just use less wattage to give the same amt of light? TS said the date code they need is on the metal plate at the bottom of the switch. None of my pictures show this letter/number code. And one last thing. I guess it's not a deal breaker but in 2007 I paid nearly 2x the price of 2 of these switches to get blue lighting vs the green led indicator lights. Only one place carried them. I forgot all about that. I'm going to call back on Monday to see if I can get the blue indicator lights :)

Joe- Your Instincts are correct: you’re gonna have a problem. Get an electrician involved before you have a fire or create an unsafe situation. I am all for DIY, except with stuff that can kill you. With all due respect, your questions, plus the workmanship like the electrical taping on the wire nuts, tells me you don’t have the knowledge or skills to do this safely and correctly.