At a basic level it's pretty straightforward. If you book a Freestyle Angle, you can:
Add the people you want in the scene Pick what you want them rated on (e.g. are they fighting? Are they talking?) Give the angle a title, that only effects how it shows up in your card (e.g. it could be "Freestyle angle between X and Y" or "X beats up Y backstage") The other angles in the angle panel are basically just that — they preset the template to follow a certain scene, and you plug in the workers. Personally I just do freestyle angles because I like the control.
A feud is just a framework that calculates all the interactions the people in the feud have. So it brings together the matches and angles and spits out a rating. When you end the feud, it adjusts the workers popularity accordingly.
People can let me know if I missed anything.