Covering the edges of plywood or melamine on your woodworking project can be done several ways. One of the most favorable is to use solid wood edging, and there are multiple ways to do this too. A straightforward method is to glue 3/4″ x 1-1/2″ strips to the plywood edge and leave it proud of the top by a hair. Then use a flush trim bit in a router to get it perfectly flush with the plywood. Doing this with a hand held router is a dubious exercise – the router is just too unstable riding on a 1-1/2″ wide strip. So do it in your router table with a tall fence. It’s safer, easier, and faster. Steve Emmons demonstrates it in this good and short video.
The traditional way to trim solid wood edge banding flush is to use your hand plane and/or a cabinet scraper. And that’s a fine method too. When you have several shelves or cabinet sides to trim flush, you’ll knock it out faster on your router table, though.