I have a student visa and you'll need to send in your formal acceptance letter from your uni to the Consulate. I didn't apply for my visa until about 2 months before I planned to leave because it took forever to get some of my supporting documents. You will also have to provide proof of payment of fees either thru loan docs or bank statements. My visa was also granted for longer than my actual course. I'm in a one year course but my visa is valid for 18 months. I have no idea why they did this.
I did my application to the LA Consulate via e-fasttrack. I then just mailed my support docs and got my visa in 12 working days.
http://www.visa4uk.fco.gov.uk/ is the link for fasttrack.
From that same site:
You will need to supply all of the following in original form or as certified copies:
Your passport (note: It must be the original document and have ample validity)
Evidence of your Immigration Status in the USA (not applicable for US passport holders)
Two photographs (passport size)
Any relevant diplomas or educational certificates which you hold (transcripts from my uni were sufficient)
A letter from the University, College or School confirming your acceptance for the course of study in the UK* and a statement of charges for the course
Evidence of Government sponsorship (if appropriate)
Evidence of funds (ie Bank Statement)
To qualify for admission as a student, a person must:
Have been accepted for a course of study in a bona fide private education institution (with properly maintained enrolment and attendance records), or an independent fee paying school outside the maintained sector, or a publicly funded institution of further/higher education*;
Be able, and intend, to follow either a weekday full-time course attending a single institution for at least 15 hours of organized daytime study per week of a single subject(or directly related subjects), or a full-time course of study at an independent fee paying school, or recognized full-time degree course at a publicly funded institution of further/higher education;
(if under 16yrs) be enrolled at an independent fee paying school on a full-time course of studies which meets the requirements of the Education Act 1944;
be able to meet the costs of the course, accommodation and maintenance (including for dependents) without taking employment or engaging in business or having recourse to public funds;
not intend to take employment or engage in business, except part-time or vacation work when given permission by the Department for Education and Employment, except see below “ Employment during periods of Study”;
intend to leave the United Kingdom on completion of studies.