The sole computer in my house is a Dell Laptop. The thing is that I want it to be wireless so I will obviously have to buy a wireless router but how can i set it up so that my laptop can find it without it being connected into another pc?
You get your wireless router, which should come with an ethernet cable. You connect your laptop to the router with the cable and set it up so that you can access the internet and also turn the wireless on. Then you should be able to connect wirelessly with the laptop.
If you have ADSL broadband, through your phone line, you'll likely need an ADSL modem+router in one.
Provided your laptop has a wireless card, you can just get a wireless router. Tell your laptop to search for networks in range and it will see your router.