I just got service today at my home... I was curious.. I have a 24" Flat Screen monitor with my computer...

Is this possible to watch satellite on?
Do I need to get another receiver?

If your 24" flat screen monitor has other video inputs, for example the Dell 2407FPW, you can use it as a display by connecting the video out from the directtv box to the monitor's video inputs using appropriate cables. Audio will have to be routed to an external receiver though, such as an av receiver.