Ok, get a sign up date in mind & then a mail out date. Usually no more than 10 days apart.
As names come in, write down all the details in a pad. Once signups close, write all names on a list as they appear in your pad & then write them all out again on a tiny piece of paper to go into a hat for the draw.
Draw one name out for each person & write the names down beside those on your list.
Pm eveyone with their exchange info & away you go........