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?
There are a variety of strategies that can get you drilling the direction you would like. One of the simpler methods requiring no special jig or prep is to begin by drilling a shallow starter hole perpendicular to the surface where you want your final bore to begin. Once a starter hole is drilled, simply reposition the drill and drill in the direction you want to go. You can dial in the accuracy by off-setting the location of the starter hole. You may want to practice in some scrap material to get the feel of where your bores will go in relation to the angles and drill size you are using. Sometimes, using a larger drill for the starter can be helpful but most of the time the same size bit can be used. With practice, one can achieve a high degree of accuracy and repeatability applying this method.
This is essentially a rough approximation of carefully chiseling an alcove in the material resulting in a flat surface perpendicular to the direction of your final desired bore.
Creating a custom pocket hole jig would be an example of a more labor intensive process up front but may be worthwhile if highly repeatable precision is desired. In that case, efficient and accurate positioning and clamping present their own learning curves.
I'm not sure how to clamp these
In certain situations you can clamp the wood and then clamp to the clamp. This was a regular use of handscrews back when they were one of the only clamps around. The workpiece could be clamped with one handscrew and then that was clamped to a flat surface with a second, to allow planing or chiselling to be done without risk of the workpiece moving when a vice was not available.
So in this case, clamp a clamp that gets a very firm grip on the wood (e.g. a C-clamp*) at a suitable angle and then you can clamp against this clamp to the vertical member you're attaching to.
Depending on the size of the C-clamp used this may not allow you to use a commercial pocket-screw jig because a smaller clamps is sure to be in the way. This may force you to drill the holes freehand by one method or another if done in situ, or you can use my final suggestion at bottom.
Even older trick
Temporarily glue blocks to the outside of a workpiece to allow clamping. Today this seems a bit odd but it used to be a common method used for assembling larger frames with mitred corners for example.
A modern alternative to glueing on blocks is given in this Q&A, How do I temporarily attach two pieces of wood together for machining?
Done right this method could definitely allow the use of a commercial pocket-screw jig.
If you find your jig can't be used...
...go a different way entirely. Drill the clearance holes in the angled pieces separately (not with them in place) and then rely on self-tapping screws to create their own pilot holes once positioned.
*Be sure to pad the jaws with scraps to prevent dents being created in the workpiece. C-clamps are very powerful and can even bruise dense hardwoods.
Another approach is to drill from the back side with the pieces off the assembly. It looks like a perpendicular hole from that side. With a small hole drilled from the back side, you can enlarge it from the front if needed and also use it as a guide to drill the pilot hole into the back piece once it’s in position.