Any advise on how to cut these two sections out of a piece of wood would be helpful.
That's a mortice and tenon. You can do it with a saw (tenon saw ideally) and a mortice chisel. It's one of the most basic and useful carpentry joints, there must be thousands of videos and books explaining how to make one.
@Airhead started
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Any advise on how to cut these two sections out of a piece of wood would be helpful.