Hooking up astro's to the computer is super easy if you have the 2013 mix amp. All you need to do is plug a jack from the livestream port into your computers mic socket. Then, in the mp3 port, plug a jack into that and connect it to your PC's headphone port.
You will need to buy a mic though, otherwise if you use the astro mic to talk, your team/friends will hear themselves and your game. You can buy decent mics for under £20.
Below, I will link one which I use to use and can guarantee amazing quality:
I thought I would be a nice guy and give you both ebay and Amazon choices, as well as giving you the correct website (.co.uk or .com) to buy from :)
Hope this helped :)