I'm trying to drill two pieces of wood similar to the angled pieces marked in blue. However, I'm not sure how to clamp these and can't drill them straight without the wood slipping. What's the best way to join them?
As the diagram mentions "pocket screws" you typically drill those type of holes using a pocket hole jig. Here is one of the more popular ones, available from various outlets: Kreg Pocket Hole jig https://www.homedepot.com/p/Kreg-Jig-Pocket-Hole-System-R3/202269070
You can clamp the jig to the material and it holds the drill bits at the proper angles to easily drill the holes where you want them.