The easy route would be a shade sail but if you're looking to construct an actual roof, that is more complicated. You'll need to check with your building department. Ideally you'd hire an architect to help with this. There are projects on Hometalk like a pergola which you can find using the search bar at the top left.
You need to be sure you have enough support for a roof. Here's a link that discusses it:
Hi! You also can buy premade gazebos and pergolas that already have a roof on them. One of my neighbors built a nice deck and added a manufactured gazebo with a metal roof. It's anchored to the deck and house, and has held up during some high wind storms. Just an alternative for you! Good luck and stay safe!
Here is a video that shows how: https://www.youtube.com/watch?v=PWV8LezJWI0
Hi! Maybe something like this would work!
Hello answers might depend on your budget.
Something like a fabric sail could be considered to be budget friendly or a pergola or retractable awning might be other options
To begin with make sure you can add a roof to your deck, you may need a building permit if it is an actual roof with shingles or metal roofing. Inspectors are "clued in" on roofs that all of a sudden get enclosed with walls. I would seriously consider getting a pergola and attaching it to the deck and house. The roof would then be up to you (no pun intended).
If you are wanting the roof over your deck to be permanently attached to your house roof, the project will be categorized as an extension, and will require building permits and inspections in order to be signed off as completed.
The completed job may also be considered a property improvement by your home insurance carrier, which may affect your premiums.
If you are wanting a cover over your deck that is not permanently attached to your house roof, then the project will not require building permits or inspections.
Thanks, ya'll! All good advice.
You will need supports on the corners. Decide whether to have free standing (4 supports) or attach to the house (2 supports). One side will need to be taller than the other to allow for a slant for run off. Add banding, then support beams/rafters, then metal roofing or decking and roofing. If you use pressure treated wood for rafters and metal roofing, put a medium like tar paper as a barrier or it will cause the metal roofing to pit and possibly rust.
Do you want a full roof or a pergola?