One tip for cutting sliding dovetails: The tapered sides of the dovetail slot tend to trap chips in the slot as you cut. So precut the slot with your tablesaw, or a router and a straight bit, as shown below, to remove as much material as you can before routing the dovetail.
To make this joint, you'll rout the dovetail slot first, then cut and size the dovetail to fit. For the slot you'll need a handheld router and the dado jig shown below.
On the Router Workshop we use spacer fences to make decorative box joints, dovetail splices,. Once the fit is correct, you are now ready to cut dovetail splices.
Using a Dovetail Jig. A special jig can guide a router to make perfect dovetail cuts in wood. Here's how to use a dovetail jig to create a dovetail joint.