Home tool for making wood edge slots?
The usual way would be to cut the grooves with a table saw and a dado set, and cut the floating tenon on the table saw as well, but for small stuff, biscuit joinery works much the same way.  You could also cut the groove with a router table.  (It would be hard to cut the groove on the edge with a router without a router table unless it's a BIG piece of wood.)