As far as I know, I am the Author (TLT term, https://thelongestthread.fandom.com/wiki/Author) with the most Threadhopping characters (I have about seven) and the one who Threadhops the most.

Ways of Threadhopping

There are many ways characters can travel between Threads. The first few times I did it, my characters just appeared in the new location. This is something I try not to do now however.

The second way my characters Threadhopped is via quantum tunnelling. I had a character, Sandy, who could control quantum tunnelling to some extent, and he just teleported between Threads, occasionally bringing other characters with him.

The third is via normal worldhopping methods, though this usually only works if the Threads you're travelling between use Cosmere mechanics. Starseeker is a character of mine who went from Sanderson Elimination to The Alleyverse via Shadesmar, though over the course of the journey, I wasn't writing him. Other magic systems like cytonics and Epic powers can also work and are more flexible, but I haven't used these for Threadhopping yet.

The fourth and easiest way (after simply moving your character) is accessing Door-Ways. Door-Ways is an RP that connects the multiverse together through doors. Characters can stumble into it, and characters that know it exists can go there intentionally by summoning a door, no matter where they are. There are only two downsides to using Door-Ways, however:

1. There are very few ways to tell what is behind a certain door unless you open it (they shuffle occasionally too)
2. Situations like right now, where someone's characters are important to what is going on in all of Door-Ways, Ashkaloda and his spider army, and they're inactive. Any characters going there could be stuck for a while from our point of view.

When to Threadhop

Now, obviously, Threadhopping is not a good idea for all Threads. It works best between Threads that are less serious and don't have fixed plots, like Battle for the Sandwich, The Longest Thread, Door-Ways, etc. I have also used Threadhopping once after the conclusion of an RP because I wanted to use him elsewhere. In this last case, it was between two serious RPs (SE and Alleyverse), but I thought that was fine because Starseeker, the character, hadn't done much in SE, and hadn't broken the 4th Wall.

Threadhopping and the Fourth Wall

Now, all of my characters except Starseeker have broken the 4th Wall. Breaking it is by no means necessary for Threadhopping - characters could see something like Door-Ways as another place that has magic doors and not a separate Thread - and most of my Threadhoppers began before they broke the wall. However, that they are part of collaborative roleplays can change how characters see Threadhopping.

Really, it doesn't matter too much for the Threadhopping itself, only how characters would react to a new Thread.

That's it for now, I'll add more if I think of anything else.