Pry out the particle board. Slip the end of a pry bar underneath one corner of the particle board and lever up. Wear safety glasses and gloves while you work to protect your eyes and hands. The board should pop off the nails easily. If it doesn't, you can cut it out with a utility knife or a handsaw.
Cut a new piece of plywood to fit. Measure the size of the area under the sink. Cut a sheet of plywood to fit this area. Use a circular saw to make your cuts. Feed the plywood through slowly and keep your fingers away from the blade course. Always use a blade guide for safety when cutting with this type of saw.
Fit the plywood into the area. If you made your cuts correctly, the plywood should fit perfectly into the space. If it's too wide, you'll need to shave off the sides until it fits.
Screw in the wood. Instead of using nails, which aren't as secure, use a drill and add a screw through the plywood, into the joists below at a rate of one every six to eight inches. Repeat until the plywood is secure.
Protect the plywood. Seal in the wood to prevent water damage and mold with a clear coat of polyurethane. Apply this with a paintbrush and let it dry. Keep a window open during this phase of the project. Let it dry and replace the items that were under the sink.