Using a circular saw, a hammer and a wood chisel, you can cut the mortise. Adjust the circular saw for the proper depth of cut. Mark the width of the groove using either the board that will go into the groove or use a tape measure and a framing square. Take the circular saw and make a number of parallel cuts between the marks. After making several passes, the wood chisel will be able to easily remove the remaining wood.
The simpler method for cutting the mortise is to use a router. With the right size route bit, the router will make simple work of that groove. It is quicker and more precise then using the circular saw.