Wait. Is this standard land based ADSL with a wireless router OR actual wireless internet (using 3G/HSDPA infrastructure - the stuff used in mobile phones?). However, you say that you don't have a router? So how's the internet getting into your house? Can you photograph the device (from the front and back) for us?
I'm assuming it's the former. This will have your router connected to a phone line. Basically, inside the router is a built-in modem that decodes the signal that's sent from the telephone line. This now usable data is then transmitted over radio signals to your computer. Generally laptops have an in-built receiver...but if not, you can purchase wireless adapters (either USB or PCMCIA) to receive this signal.
With the latter (3G/HSDPA), data is sent using a carrier-supplied modem over the mobile phone network.
I know I'm using the wrong terminology, but it's in the interests of keeping this away from tl;dr.