Determine the trellis' final dimensions - it should be big enough to look like it belongs in its proposed space without overwhelming the area.
Choose redwood or cedar for outdoor structures; pressure-treated lumber can also be used. For this trellis, use 5/8-inch by 1 1/2-inch pieces for the uprights and crosspieces, 2-by-2s for the side pieces and bottom of the frame, and a 2-by-6 or 2-by-8 for the top piece.
Cut the upright pieces to the desired length. Lay them out on the floor, face down, with the correct spacing between them. For the most pleasing look, use an odd number of uprights.
Cut the crosspieces to the correct length and lay them on top of the uprights, spacing them evenly. Place a small bit of waterproof glue where the pieces cross, and then attach the crosspieces to the uprights at each intersection with nails or screws.
Cut the top piece to the same width as the grid.
Cut the side pieces of the frame. Side pieces should measure the length of the grid plus the top piece, plus any additional length for setting the trellis into the soil or a container.
Attach the side pieces to the sides of the top of the frame with glue and countersunk deck screws.
Slip the grid into the frame between the side pieces so it rests against the bottom of the top piece of the frame. The back of the grid should sit evenly with the back of the frame; the front of the frame will be a little wider than the grid.
Cut a 2-by-2 piece of lumber the width of the grid and slide it into place against the bottom of the grid, keeping the backs even. Attach with glue and deck screws. Add additional screws at the back of the frame for added support.