Click on "Export account" to save your account data.
Save the file in a secure place! It contains your details, your contacts, groups, and personal settings. It also contains your secret keys to authenticate yourself to your contacts.
Go to your new server, and open http://newserver.com/uimport (there is not a direct link to this page at the moment).
Do NOT create a new account prior to importing your old settings - uimport should be used instead of register.
Load your saved account file and click "Import".
After the move, the account on the old server will not work reliably anymore, and should be not used.
Friendica will recreate your account on the new server, with your contacts and groups.
A message is sent to Friendica contacts, to inform them about your move:
If your contacts are runnning on an updated server, your details on their side will be automatically updated.
GNU Social contacts
Contacts on GNU Social will be archived, as we can't inform them about your move.
You should ask them to remove your contact from their lists and re-add you, and you should do the same with their contact.
Newer Diaspora servers are able to process "account migration" messages.