Make the cuts according to which size of lantern you are making. See steps 2 and 3 for detailed views of the legs and rails. You might find it easiest to sand all of the pieces before assembling the lantern.
Using a compound miter saw, cut the 4 legs (18” or 30”) with a 5 deg miter angle and 5 deg bevel angle (head tilt) on both ends of the legs.
Cut the horizontal rails with a 5 deg miter angle on each end, the miters need to be opposite direction from each other, making a trapezoid. It is best to trim the two corners that will face the inside of the lantern. I set the miter saw at 45 deg and removed about ¼” of the corner material.
The lantern top is made from the 4 shorter rail pieces and the short 1x4’s (7 ½” & 6” or 4” & 2 ½”). Center a 1x4 piece on a short rail piece, making the bottoms flush and glue and nail into place. Repeat for each rail. Glue and nail the four 1x4’s together making a box.
Assemble two legs to a long rail. The rail bottom and leg ends should stay flush. I prefer the outside top corner of the rail to be flush with the outside face of the leg, purely for looks. Apply wood glue then clamp a leg to a rail, predrill a hole and screw the leg to the rail. Repeat for each leg.
Attach the two leg assemblies the same way as the legs are attached to the rails. Apply wood glue then clamp a leg assembly to a rail, pre-drill a hole and screw the leg to the rail. Repeat for until all four sides are secure.
Attach the legs to the top. Apply wood glue then clamp a leg to a short rail, predrill a hole and screw the leg to the rail. Repeat for each leg. I decided to drop the top about 1/8” from the top of the legs to add variation.
Turn the lantern upside down and layout the planks (10 3/8” or 16”) for the lantern bottom. Trim the 1x4 planks as necessary, I left about 1/8” overhang around the bottom. Apply wood glue and nail the planks to the lantern base. Attach the feet to the bottom with wood glue and nails.
Sand the lantern until smooth, finishing with 120 grit sandpaper, always finish sanding in the direction of the grain. Apply wood conditioner and stain to the lantern. Once the stain is dry, you can distress the finish as desired.
Drill 2 holes through the top 1x4’s. Thread a rope through the holes and tie knots on the inside of the top. Add decorative nails if you want to cover up the screw heads.