I have a drool machine for a son. So I decided to make a bib today. I had a little scrap of pre-quilted fabric (not the cutest pattern, but I'm really trying to use things in my stash, so it works). I used a store-bought bib as a pattern to cut out the shape. Then I just sewed some bias fold tape around the edges, added velcro and PRESTO!
I also made another bib (no pics, sorry!) by cutting out two pieces of cotton, sewing them together and flipping them right side out. However, if you have a very soggy baby like mine, this bib will only keep his clothes dry for 20 minutes. So I'll have to take it apart and add a layer of batting or flannel inside.
If you want to make a bib or two (or ten) for your little slobberer, here are a few other tutorials I've come across:
Vinyl Tie Bib
Asymmetrical Button Bib
Basic Velcro Bib
Bias Tape Bib