I need to connect a computer to a wireless network, how?

Well, my uncle bought a desktop some time ago, and he asked me to come fix the internet for him

I don't know that much about it, but maybe you guys can help.

Facts:
- He is an internet abonnee, my nephews laptop gets connection in the house
- He has a working wireless router (can't put internetcables into that router to connect the pc like that)

So it has to be wireless (desktop is like 10 metres away from the wireless station)

So now I need to hook that desktop up to the wireless internet, how do I do that?

Probably I'll have to buy a ethernet card or something similar?

Are there different options? Like one you can plug in with USB, or one that you have to install somewhere else?
Will all options work on an average computer, like do I need special ports to install such a device?
How can I see which options will work on that computer when I visit my uncle tomorrow?
What do I buy in the shop and will most likely work?

Thanks guys if you could help me out here

But how do I know if that PCI thing fits in the computer?

I can't just buy anything in the shop and asume it will all fit or can I?