Lattice typically comes in 4' x 8' sheets. If the posts under your deck are more than 4' apart, you may want to install non-load-bearing posts at 4' intervals. Cut 2" by 2" supports to fit the length of the deck posts as well as the area along the bottom of the deck between the posts. Attach the supports using exterior-grade deck screws.
As an alternative, use H-molding to seam pieces of lattice together (Image 1). If you use H-molding, you'll need to install a stake at the bottom to hold the lattice in place.
Use a circular saw or jigsaw with a carbide tipped blade to cut the lattice. When you make your measurements, allow 1/4" on either side to allow for expansion and contraction of the panels. If you have a slope, you will need to cut the lattice to match the grade. You could also extend the lattice a few inches into the ground.
Measure and cut sections of lattice U-molding to fit each space. Make an inside miter cut on each corner.
Cut the lattice panels to size with a circular saw or jigsaw with a carbide-tipped blade (Image 1). When you make your measurements, allow 1/4" on each side to allow for expansion and contraction of the panels. If you have a slope, you'll need to cut the lattice to match the grade. Another option is to cut the lattice so that it extends a few inches into the ground.
Snap the molding onto the lattice (Image 1). Set the panel and molding in place, drill pilot holes through the molding (Image 2), and secure the lattice with screws (Image 3).
Create a 2" by 4" support for the door. Toenail the top of the support into the deck (Image 1), and secure the bottom of the support to a stake after checking the support for plumb (Image 2).
Measure the opening for the doorway, allowing 1/4" on each side for expansion. Make a door frame out of 2" by 4" boards. Attach the boards with deck screws (Image 1).
Cut a lattice panel to fit the door frame, and attach lattice trim around edges. Miter the corners of the trim for a more professional look. Attach the lattice to the door frame with galvanized screws.
Attach hinges to the door (Image 1), and attach a handle (Image 2) to the outside. Attach the hinges to the door support to secure the door (Image 3).