How is a multi-angle scene filmed?
Shows can be either "Single camera" or "Multi camera."  Sitcoms, shows broadcast live, and stuff shot in front of a live audience is generally multicam -- they do it once, or as few times as needed to get a good take.  They just have three (or however many) cameras, and cut between them.

Other stuff is Single camera.  Some "Single camera" stuff actually has two cameras rolling when it's convenient, or maybe a rare action shot where they had a whole bunch of cameras running to capture an expensive stunt or something, but it's still considered single camera style work.  I expect Better Call Saul is shot this way.  Basically, you do many "setups" where you typically tweak staging and lighting for each camera setup and do the scene or part of the scene over and over.  There is usually some piece of equipment just off screen in any given shot like a light stand or a boom mic so each shot is as nice as they can make it, but if you shot it from another angle at the same time you'd see equipment or crew, or it just wouldn't look as nice.  People and objects get moved around between shots to get nice framing, and you never really notice that a table moved a few inches or whatever.

As for how many times, ultimately the director decides.  Some directors are lunatics, and a certain scene in a film with a long schedule may get shot hundreds of times for variations on performance, angle, etc.  Some directors are more efficient and a scene might only get shot like a dozen times if you do three takes for each of four angles/setups.  Some directors will work closely with their crow in deciding these things -- often the cinematographer will have a lot to say about how many angles they need to get to cover the whole scene, and which shots will be most interesting.  In a few rare cases, a whole scene will get shot just once, if it's something that is a big expensive stunt.  If you only have one car, you can only blow it up once, so you just have to try to get it right.  There was a scene in the documentary TV series Connections where the presenter timed his monologue to the countdown timer of an actual NASA rocket launch of a space probe that was visible in the background.  Obviously, they could only get that shot once because you can't go to NASA and ask them to quickly launch another 100 million dollar space probe because you got a little tongue tied.  Though, I assume they got a few takes without the rocket launch as well.