Any suggestions? Is it the same as setting up wi-fi here in the US? Is there a certain company that is best/cheapest/most reliable?
It's pretty much the same as setting it up in the US. Whatever ISP you choose will check to see if the flat has a BT (British Telecom) land line installed. If there's not one, you'll have to get one installed. I'm sure they can set that up for you, but I don't know how expensive it is.
If there is a BT line, then it's just a matter of picking an ISP and ordering broadband. Most of them throw in a wireless router with a new account (I've never heard of one that doesn't). It usually takes about 10 days or so from the time you call and order the service for it to be turned on.
I had Sky broadband for the first couple of years I lived in the UK, and Sky sucked. The speed was terrible, the line dropped out all the time, and they totally screwed up moving our service from one house to another when we moved. (Search my posts for "sky" and you should find a few good rants.)
Later we switched to Plusnet, and they've been great. The service is cheap, when it dropped out a couple of times at our last house, they were very good about getting someone out to check what the problem was and getting it fixed, and when we moved a few weeks ago they got all aspects of moving our service from one house to the other exactly right, and exactly when they said they would. I recommend them highly.
This website is a good one for finding a deal which will work for you (click on the phones, TV, & broadband tab):
http://www.moneysavingexpert.com/utilities/