The tools you need are:-

1. Tenon Saw
2. Try Square
3. Marking Gauge
4. Pencil

Take one of the pieces to be joined (A) and lay it down flat on your workbench, then take the mating piece(B) and lay it on top in the opposite direction, making sure the edge of piece (A) is flush with the end of piece (B) (as shown on the left <- ).

With a pencil, mark the width of the timber onto piece (A) using the mating piece (B) as a guide.

Remove the mating piece(B) and put it to one side.

With a try square follow the line you've just drawn, all the way round the piece of wood (A).

Repeat this with the mating piece (B).

Set your marking gauge to half the thickness of your wood.

Gouge a line on both edges from the line to the end of the wood. Also gouge a line on the top of the pieces (the end grain)

As I said before "A good tip so you don't go passed the line is to put a small indentation just before the line using your marking gauge - so when you gouge the line, the pin on the marking gauge should fall into it, therefore stopping you going too far" and "When using the marking gauge it's best to hold it at a slight angle and to take several light passes. By doing this you should be left with a nice straight gouge line".

Re-clamp the work piece at a 90° angle. Then saw from the top all the way down to the width line. (left <-)

Unclamp the piece and follow this step and the step above onto the mating piece (B).

Cut along the 'across line' until the waste pops out ( <- Left ) After that clean up with a chisel if needed.

Do the same thing with the mating piece.

You can use your bench vice or even a workmate for this step but I used a bench hook.