Praise be to Allah (The Glorified and Exalted).
Marriage in Islam is done in the following manner:
1) The girl needs a wali (guardian). Usually this is the father, but a non-Muslim cannot be the guardian of a Muslim girl. Therefore, revert women must use their local Imam or another Muslim that is not related to the groom, to be her guardian.
2) A marriage contract is drafted and agreed upon and signed by both the guardian and the woman he represents and the groom.
3) Two witnesses that are Muslims must be present. There are some rules concerning who can be a witness. You may learn more by the link, I've provided below.
5) Then the guardian of the woman says, "I give so and so in marriage to you (groom), do you accept.
6) Then the bride and groom hold a feast for the local community or few others, which should not be too extravagant and which should include some of the poor. Usually Muslims hold a feast for their local community. And the marriage is announced to the local Muslim community.
Learn more at the following links:
http://islamqa.com/en/ref/113867/marriage
http://islamqa.com/en/ref/40290/marriage
http://islamqa.com/en/search2/marriage/AllWords/t,q,a
And Allah (The Glorified and Exalted) Knows Best.