Remove all offending material that is sagging until you reach quality wood. For bench seats that have been nailed in place, you will need to use a combination of a hammer and pry bar in order to remove the pieces of wood. Use a drill to reverse the screws, if the wood has been screwed in place.
Measure the pieces and purchase replacement material at your home improvement store. Alternatively, take some of the scrap material into the store with you so you can accurately pinpoint exactly what type of material you will need to purchase to replace the old.
Cut your material down to size using the miter saw as required. Measure and mark the pieces with the tape measure and pencil, or use the old pieces as a guide. Place a piece of wood on the tray of the miter saw, align it with the fence and then pull the trigger while you pull the blade down through the wood.
Install the new material in the order that you removed it. Braces are installed across the bench first, and then the actual seat material is installed on top of the bracing. Finish the bench according to your personal preferences to match the rest of the material, such as with paint, stain or natural oil.