You'll need a wee bit more than that I'm afraid!
Here's the link to the IND website that will you all you need to know:
http://www.ind.homeoffice.gov.uk/ The short story though is that you'll need to apply for the visa from the US, and your fiance will need to send a letter of support (ie, a letter saying she's agreed to marry you, etc) as well as her passport. Together you'll need to satisfy the consulate's office that a) your relationship is legitimate, that you've met in person and you plan on marrying within six months and are planning to live permanently in the UK, and b) that you have the resources to support yourself without having to rely on public funds (such as benefits).
Oh, and you'll need the fee, which I think is somewhere around $500 at the moment.
As for timing, if you can go to the consulate in your area in person, it is likely you'll get the visa the same day. Alternatively, if you do it by post, it will take a couple of weeks (as long as your documentation is all sufficient.)
There's tonnes of info here about people who have gone through this so do a search here on the forum for more info and stories to help.
