I have been to Christian weddings (American), Jewish weddings, and Hindu weddings, but I have no idea what a traditional Buddhist wedding looks like. I realize that there are probably differences between the different sects of Buddhism, but are there any common cultural threads?
Here in Sri Lanka, the couple go to a Buddhist temple to get the blessings before or after the marriage ceremony. The festivities are mostly cultural. But if you really want to do it the Buddhist way, don't serve liquor or kill animals for your wedding. Also, don't get into debt just to make the ceremony grand.
A marriage is something that increases attachments to this world, and Buddhism encourages to go in the other direction on reducing attachments. So, Buddhist monks or Buddhist monasteries do not play any role in marriages at least in Theravada. Of course, the monks would give their blessing to the couple as in any other special occasion in their life when they visit the monastery before or after the marraige, as mentioned by Sankha.
Weddings are taken according to local customs of the people involved in it. The closest that happens to a religious activity during a wedding is the chanting of paritta, Jayamangala Gatha as a blessing to the couple. This is also performed by lay people. Another influence of Buddhism in a marriage I would say is that the couple would bow to the parents as you would bow to a monk or a Buddha statue.
Recently in Sri Lanka there were some attempts to have weddings in a temple, and it got criticized by monks and the public (I don't know the current situation though).