No. 1: Get urself a bt account, v easy if you already have a line going into the flat. Just ring 0800 800 150 (from any phone) to get it activated. The cheapest package is £9.99 a month. Once that is all setup..
No. 2: Go on the internet (at ur mate's house or in an IT classroom) and sign up for one of the many ADSL isp's. I recommend pipex. It costs £23.44 a month, its fast and quite reliable. If you dont have an ADSL modem already, you can get one for just £17 with their solo2go package. Their address is:
http://www.solo.pipex.com
One word of warning - if you only have your flat for 9 or 10 months, you are going to have to pay to get out of the contract at the end of this time, cos you haven't used 12months. (I think it's £50 cancelation fee).
One more thing - when you call BT to initially activate your line, they'll probably try to sell you their own broadband service, 'bt broadband'. I personally wouldn't recommend them as they charge more per month (£28) and more for the modem (if you need one).