How do actors doing cameos normally come about?

Sometimes the actor is a fan of the show and requests to be on it, like Prince in New Girl, or most Simpsons guest stars. Other times the actor happens to know someone in the cast or the creator and they simply ask, or they’ve worked with that actor in the past and wants them in the project again for a random cameo cause they’re friends James Gunn does this a lot. So yeah, it’s both.

Sometimes they are invited by the showrunners. Sometimes celebs are fans and ask to do a cameo. Sometimes celebs are dating someone in the show and are asked to make an appearance. Somtimes celebs are filming on the same lot location and ask to or are asked to shoot a cameo scene during their downtime on the lot.

Brad Pitt did Friends because of his wife Jennifer Anniston. Robin Williams and Billy Crystal did one scene on Friends because they’re were filming a movie on the same set

Basically once you are established as an actor you are part of the scene, you hang out with people in the industry, whether it is at parties or dinners, and so on. So making the connection isn't that hard as they have contacts who know people who can get in contact with the show or the actor. Sometimes the actor pushes for the opportunity. The are famous people just being stormtroopers with their helmets on, including Daniel Craig, Tom Hardy, Princes William and Harry, and Ed Sheeran. After The Big Bang Theory made fun of Stephen Hawking he reached out to get on the show. Other times shows reach out looking for others. In Thor: Ragnarok they reached out to Matt Damon, Luke Hemsworth and Sam Neill to play the actors playing the characters in Thor in the play in the movie. Obviously Taika Waititi knew Sam Neill as they are both New Zealanders and they only have a population of 4 million, while Luke is Chris Hemsworth's brother and Matt Damon is Chris's friend. Often it is a push/pull situation, with shows with cameos attracting more people wanting to do cameos but they would also be reaching out to get people into them. Again, personal connections matter.

They know guy that knows a guy that knows another guy

I'm guessing the actor usually makes the first move.

Depends on the show truthfully. Usually the actor doing the cameo has worked with someone involved in making the show so it’s as simple as a phone call saying “hey I’ve got a role that you’d enjoy that would only take up a day or two” or their agent may reach out to the show and say they’re a fan and would like to cameo if timing ever works out.