A bucket with a hole is as useless as a pool without water. Plastic buckets eventually get holes which must be sealed. While most people just go out and buy a new bucket, fixing a plastic bucket with a hole in it isn't as difficult as you might think. If you've got the time it's best to fix it yourself and save some money.
Prepare the bucket for repair by cleaning and drying it and looking closely at the hole. The more you know about what you're dealing with the better you'll be able to fix it.
Determine if it's a big hole or a small hole. A big hole would be anything larger than a dime.
Repair the hole with epoxy if it's small. Apply epoxy over the hole, following the instructions on the tube. Be careful to keep epoxy away from children.
Repair the hole with a piece of plastic and industrial strength glue if it's larger than a dime. Cut out a piece of plastic the size of the hole and apply the glue. Press down on the piece of plastic until the glue has dried.
Melt a piece of plastic onto the bucket over the hole if the glue doesn't hold. You can use a soldering iron or a piece of heated metal. Use your fingers to mould the melted edges over the hole. Be careful not to burn your fingers. Use gloves if necessary.
Fill the bucket with water to see if you've successfully patched the hole. If it leaks water, try again or throw the bucket away and buy a new one---not all buckets can be fixed.