The card is a lot like a VCR. You will have two inputs to the card the names will vary. One of them is the coax connector (antenna) the other is the Svideo connector (aux, cable, etc).
Per what Sazar, said hook the RCA plugs from your Dish receiver to the adapter box and then plug the svideo into the ATI Card. If it's a white box AIW you may only have a cable with svideo on one end and 3 RCA plugs on the other. Hoperfully they didn't stiff you on the adapter cable. If they did it's radio shack time. The RCA plugs are sort of color coded. Red usually goes to red (one audio channel), yellow to yellow (video) and black/white (other audio channel) go together.
Use the AIW software to select the Svideo input (could be called Aux, cable etc) as your input source. Turn the dish receiver OFF and then have the software auto search for sources. This will find any local TV signals that are passed through the receiver. Now manually add channel 3 (in most areas) or possible channel 4.
Turn on the Dish receiver and select channel 3 (or 4) on the PC and you should see your Dish program.
If you want you can hook up an antenna to the coax input and, select that input (probably called antenna), do another search for signals, and the card will be set up to receive braodcast TV also. This will allow you to use the PC for one source (Dish or Antenna)) and your regular TV for the other.
Don't forget to set the input source to what you want to record/watch (Dish or TV).
PS You will probably need to run the Audio Out from the ATI card (small plug) to your Audio Card to be able to play the sound on your PC.