Building a deck on a slope presents several problems. The ground is not flat, so you can't simply build a level structure. You have to account for the slope grade and be sure the deck is stable and secure. This problem is one reason many decks are not built on slopes. However, since slopes really have no use and can't be enjoyed or grilled on, building a deck over it is a big asset. It adds a nice, flat area your family can enjoy and improves your home by adding another liveable space.
At the top of the slope, dig two foundation holes that are about 1 foot in diameter and deep enough to find solid soil (about 1 to 2 feet deep or more). These holes will hold the supports for one side of the deck.
Install a deck post in each hole. You should measure each post to the height of the deck on this side, with about 1 additional foot of post on each end. That will be cut off later, once the final height of the deck is determined.
Fill the holes with concrete and let dry. Make sure the posts are level by testing them with a water bubble level as the concrete dries.
Attach a string to each post and extend it to where you want the opposing side of the deck to be located. Leave the strings there, then mark on the ground where the support posts should go.
Dig two more support holes for the other end of the deck at the low end of the slope. Now install two long deck post beams in these holes. Hold the string up to the posts to ensure they are long enough to support the deck. Then fill the holes with concrete and level them as you did in Step 3.
Tie the string to the posts at the intended height of the deck, so you have a guide for the floor beams. Hold a level to the string to ensure it is straight and true. Then make a mark on the posts to indicate where the deck beams are going to be secured.
Attach deck beams to the posts with 3-inch nails or bolts, using the mark as a reference. Frame both sides, the front and back with 6-by-2 inch beams or your chosen type of board.
Attach your floor beams to these deck beams using metal braces or 3-inch nails. Then lay your deck boards down across the beams.