I usually create a repository with with a test runner already set up and the kata description as a text file. In advance, I ask the participants to clone the repo, run the tests, add their name to the readme, and commit and push. This is to confirm that the project can run on their computer and they have access to the repository, so we don't have to spend time debugging that once we start the session.
To rotate driver during the session, current driver commits and pushes. Then the next driver shares their screen, pulls the latest changes, and runs the tests to confirm that they are in the same state as before. Then we can proceed with the kata.
I prefer screen sharing over tools like VS Live Share or Code With Me (IntelliJ). 1. They do not share other things that might be going on on the driver's computer, like a web browser; 2. they don't even share everything that's happening on the driver's computer inside the IDE (e.g., tooltips or popups won't appear for other participants); 3. at least in Code With Me, the automated refactorings are not available for "guests" (at least they weren't last time I used it).
Even mediocre screen sharing like Teams is OK and can be good enough, but something like
https://tuple.app/ is better (also pricey). If using Tuple and you have sufficiently low latency, I would even consider running the IDE on one machine and letting the driver use it remotely. With Teams, I would recommend everyone runs the IDE locally and shares their screen.