Some speakers are wireless, so hooking them up might be a little different. Normally you place your speakers in the desired spots and hit a button to connect the speakers together wirelessly. There should be a button on the receiver and on each speaker that need to be pressed to do this. Once these are all connected you simply need to plug the receiver into the computer.
A lot of the nicer systems also come with their own software to help your computer manage their awesomeness. Check and see what is included with the system; if there is a disk then you should run the software installation prior to connecting the speakers.
For the more advanced speaker sets you will find that there are several cords that are the standard headphone size but are different colors. If this is the case then you will need to plug in each individual speaker set into different ports. They are as follows (pictured above)
Green: front channles
Gold: center and subwoofer
Gray: side channels
Black: rear channels
The two remaining hookups are for microphone input (pink) and audio input (blue). You won't need those here.
To have your computer read those hookups you will most likely need additional software. Most of these speaker systems come with this software packaged. However, in many cases the type of sound card that came with your computer is not powerful enough to drive these advanced speaker sets and you will have to buy and install a new sound card. This gets a little complicated but you can follow this guide over here.
Once again, once the speakers are connected make sure that both the drivers from the Operating system and the audio card are set for the right speaker system. With this you should be set! If you've been through all this and things still aren't working try this guide to fixing computer speakers to see if you can resolve the issues.
Alright, well hopefully you're up and running! Don't annoy the neighbors too much with your incredible system.