You might want to take a look at
www.britainusa.com and
www.ukvisas.gov.uk. My suggestion is that you get a co-sponsor as your fiance is a student. Maybe his parents? All they need to do is write a letter stateing that they will support you financially if he cannot, and provide their last few months bank statements. Other than that you'd need;
Two passport photos of you, face-on
Fee I think £250 in USD equivilant
Application form
Proof of marriage to take place eg cert of provisional booking for wedding, receipt for engagement ring
Photos of you two together to prove you have met, phone bills, emails, boarding passes etc (not too much stuff, just 2 or 3 of each)
Both your passports, or yours plus a certified copy of his (every page must be copied)
Statement of support from your sponsor (the Brit) that he intends to marry you within 6 months and you will live together permanently as husband and wife
Proof of your accomodation in the UK (house deed, tenancy agreement etc)
Proof you can be supported without recourse to public funds (bank statements showing his regular income, or savings for either of you).