Round holes can be easily made using a router with a circle cutting jig. There are many that you can buy at Home Depot, Lowes, or your local hardware store. Alternatively, you can easily make your own circle cutting jig with some scrap plywood or MDF and a few nuts and bolts. There are many plans readily available with a Google search.
After mounting your router to your jig, place the pivot point in the center of the circle that you want to cut out, then adjust the jig to your desired radius. Set the router bit to the appropriate depth generally starting at about 1/8”, slowly rout your circle and repeat as necessary lowering the bit with each pass. It’s generally safer and easier to cut outer edges of circles in a counter-clockwise direction, and inside edges clockwise.