Depends on what you want to do with the tv in the basement and how many sat receivers you are running,............
We are running 2 HD recievers from directv, 1 in the living room, 1 in the bedroom.....
The bedroom reciever is in the cabinet beside the tv. I simply run the small tv in the bedroom with an s video and audio cables. From the back of the reciever i ran an HDMI cable (20 feet long, A little pricey) down from the cabinet (behind the curtains) beside and under the dresser (right along with the W/D plumbing) and out into the basement. Plugs directly into the 42" tv in the basement. You will need to make sure you have RF remote controll for your sat reciever in the bedroom (as opposed to an IR remote) and that the reciever will work with an RF remote. This will allow you to change channels and so forth from outside the rv. The RF remote is well worth the money and is available from your sat provider, doesnt have to be pointed at the receiver to work.
This is the way I did it, Definatly not the only way to do it. We rarely ever use the tv in the bedroom, (may have been on once in the last year) so we didnt have to have it hooked up, but I didnt want to have to move stuff or unhook and rehook cables when the wife wanted to use it. So I went this route so everything is always connected. Only downside is bedroom and basement tv have to watch the same channel on sat, like I said that isnt a problem for us.
Dont know what system you have, whether you already have it hooked up, or how many recievers you are going to run. There are alot of different options, and alot of knowledgeable people here that can help you figure it out if you run into a problem.
Good luck,
Wesley