@hache I just did it for the first time. It was easy!
1. Create an account on the desired instance.
2. On the old instance, go to Settings → Data Export, and export the things you wish to keep.
3. On the new instance, go to Settings → Import, and import the files you get from step 2.
4. On the old instance, go to Settings → Edit Profile, and find "Move to a different account," press "configure it here," and enter your new account.