It's a pretty simple design:
Here is the progress so far...
The main beam is built up of three 2x8's glued and nailed together. Here is how I calculated the needed beam size:
The ledger on the house took longer to get in place than I thought it would. I took my time to make sure it was square, level and centered with the beam I put up. I attached it with 1/2" lag bolts on 32" centers. If this isn't installed very level and even, then getting everything else lined up later on will be painful.
I decided to go with a 2x8 ledger, so I could attach a 1x2 lip at the bottom for the rafters to sit on. I did this for two reasons: It makes holding the rafters much easier when you are attaching them, and it covers the bottom gap where the rafters meet the ledger. I noticed this on a number of patio covers I looked at.
The rafters are attached to the beam with L-brackets and then lag bolted through the tops in to the beam.
Helpful documentation that I used to design the patio cover:
From these three sources, you should be able to spec an appropriate cover for your area and design choices.