Sacred said:2) How do I connect to the internet using a different modem? (as in how will the modem know where to connect to, its not like dial up as in I dont have a number )
Tesco should be able to give you your username/password etc. (probably it's on the stuff they sent you when you got the account) - the Quick Setup Guide that comes with the modem walks you through the setup for a standard BT phone line with ADSL.
Sacred said:3) What would I need to have my PC connect to the wireless internet connection (and for the love of god I hope its cheap)
No need to go wireless with the PC (unless you want to), use an ethernet cable - the modem I linked to has 4 wired ethernet ports on it as well as the wireless connection. Cost £1.39 for a 1m lead from Solwise. I'm assuming your PC has an ethernet port - most fairly new ones do!
If you don't want to go wireless with the laptop either, you can get a wired ethernet-only modem for £30-ish as stated above. Wireless is great with the laptop though as you can use it throughout the house. Don't forget to secure your wireless network though:
http://www.jiwire.com/wi-fi-security-introduction-overview.htm