Add the footings and the beams with cross bracing.
Draw the deck outline on the grass with marking paint and remove the sod from the area. Lay out footing and post positions with mason line according to your design. Rent an auger to dig 10-inch-diameter holes for footings (this is six inches deeper than the minimum depth required by some codes). As you dig each footing hole, insert a 10-inch cardboard footing form and back-fill the form with sand. Call for the footing inspection after you dig all the holes.
Mix concrete in a wheelbarrow or rented mixer. Fill each footing form and settle it with a 1x2 to remove air pockets. Screed the top of the form with a 16-inch piece of 2x4. Insert a J-bolt into the wet concrete where the post bracket will be.
Use pressure-treated lumber for all the framing.
Add post brackets and posts once the concrete has set, usually 24 hours. Attach the posts to the brackets with the recommended nails. Post-to-beam brackets go on top of the posts to hold the beams. Add the beams and secure with more nails. During installation, use a level to ensure that every post is plumb and every beam level.
Use skewable joist hangers and angle brackets to connect angled joists.
Build the joist frame of 2x8 lumber. Start by laying the joists across the beams in their approximate positions. Mark two side rim joists for 16-inch center spacing. Add joist brackets and attach the joists. Do the same on the other side.
Around the pool, add angled joists and blocking to accommodate the pool's curve. Deck boards can overhang the joists as much as six inches, but no more. Secure the joists to the beams using appropriate rafter ties.
Install 4x4 posts on the inside of the joist frame with 1/2-inch carriage bolts. Ideally, posts should be installed to the rim joist and joist, or rim joist and blocking. Use a post level to keep the posts plumb. Call for inspection at this point if your local codes require it.
Add blocking in between joists to keep them from twisting.
Install decking perpendicular to the framing and running toward the pool. Space boards 1/8-inch apart and secure with 2-inch deck screws treated for the type of decking you are using.
The curve of the pool is cut by cutting each deck board individually. Place the board in position with the proper spacing and butt it up against the pool trim edging. Mark the cut line as a tangent to the pool curve. Use a combination square to measure the resulting gap on one side of the board, and transfer it to the other side. Draw a line from the mark to the corner of the board and cut. The end of the board is now a tangent to the pool curve. The sum of the tangents will be a curved edge. Install the deck board with a 1- to 2-inch gap between the board end and the pool trim edging.