Are you saying that bits of the belt went through the timing belt cover? If so, like one of the members above said, make very sure that you get all the pieces out.
You should inspect all pulleys and see if they are straight and true and tight. If the belt broke from age, then it's simply a matter of replacing it. While you're at it, replace all of them. How many miles are on your car? It may be due for a timing belt change, which should be every 60,000 miles, if not earlier. If so, you should also replace the water pump, balancer belt, its tensioner, and timing belt tensioner. If the balancer belt fails, that will cause major engine damage. If you don't know when the last timing belt job was performed, you should do it just to be safe. All that, along with new accessory belts will run you $500 to $1000, depending on where you go.