First, send out a newsletter asking parents to send in a picture of their family. Send this newsletter out a good week to two weeks in advance. Point it out to parents when they pick up the newsletter and bug your parents the night before the project. As most teachers already know, sometimes parent participation is very difficult to ascertain.
The day of the project, give each child a piece of cardstock. You can make it as large or as small as you want, rectangular or square, but I do recommend heavy-duty scrapbooking paper above construction of printer paper. Ask each child to draw a picture of their family. When each child is done, ask if you can label the child's drawing (always ask to write on a child's drawing! Some kids go nutty if anyone touches their artwork. I should know because, back in the day, I was one of those kids). Label each "person" they drew (even if they're just "scribbles").
Take what pictures the parents gave you and glue them (or have the children glue them) onto the back of the picture. Punch a hole in each corner of the cardstock. Arrange them side-by-side on a table until you have the quilt layout you like. Use string or ribbon to tie the corners together (when down correctly, it'll look like you have a string-square at every intersection). Tie two long pieces of yarn to the top corners and find a good spot on the ceiling to hang it.
*Don't mind the psychedelic spirals. I figured it was less of an eyesore than black circles.