The following directions are for one option only. Please know that you have many options and building styles to choose from; don’t hesitate to dive in and explore and ask questions.
The most important thing you can do, prior to building your palapa is to plan things carefully. Plan properly to avoid mishaps and poor construction. It can be difficult to remove and/or relocate a palapa so get any input available to you and find a proper location. The ideal spot for your palapa should have nothing overhanging and the ground must be free from obstructions. Be sure to contact your utility company if you need to do any digging. So you’ve made proper plans, discussed your options with family, friends, and your local tiki hut masters; be sure you have footings in place before you start building.
The Palapa posts and beams may be heavy and awkward so be sure to have trusty, strong helpers to assist. An "A" frame helps to stabilize the posts while leveling and plumbing. You might choose to elevate the posts off the patio using adjustable post bases. By doing this, you get the post off the floor and ensures it will not decay from water damage. This also makes the structure "portable". This can come in handy depending on your local zoning ordinance. Galvanized lag bolts help to fasten all the framing together. Once you have the framing in place you can start "stringing" the latillas or prepping so your thatch will have support or something to lay on. (A latilla is a limb or thin pole, used as a ceiling material between beams). Depending on the design you choose, you may or may not use them.
Some folks have the latillas exposed with the bamboo reed or thatch sandwiched between the roof sheathing and the latillas. Your roof can take on it’s own unique character depending on the materials you choose. Bamboo, plywood, thatching, and a variety of other options will help serve you. If you are using latillas, once the latillas are in place and fastened together, lay the reeds or thatching across the latillas prior to stapling the plywood down. Be sure that someone is watching to be sure your reeding or thatch is in place before you fasten it.
Again, do the research and enjoy yourself! Your needs may differ and lead you to a whole different palapa experience.