I haven't used this drum kit, but from what I read about it, it basically sends midi notes to your PC, so it's in a way like a MIDI controller.
You would first of all need a sound card with ASIO support. The point here is that your ordinary, cheap sound card driver has massive latency and you don't want that, because you'd be hearing all the sounds of your drums delayed. You can also check whether you can get away with using the ASIO4ALL driver, which is free, but you might not get acceptable latency with it.
The other thing you'll need is software generating the sound. Take a look at stuff like Steven Slate Drums, EZDrummer, Addictive Drums, etc. There are some free alternatives out there, but I never was quite satisfied with them and Steven Slate Drums are imo the best thing out there and you don't have to go for the most expensive version.
Last but not least, depending on whether your drum SW comes with a stand alone application or only as a VSTi, you might need a host. If you need one, I'd go with Reaper, which is cheap, but also has endless trial iirc. There might be free stuff out there, idk.
So basically:
1) connect to PC via USB
2) open up standalone drum SW or load VSTi in host
3) configure standalone or host to use ASIO soundcard/driver
4) play some sick metal beats
If you don't understand stuff like ASIO, VSTi, etc., google will give you some usable results.