You can request an account on this server by sending an email to 'slugmax _at_ tilde _dot_ team' with the subject 'Republic new user request' and containing your requested username and SSH public key. You'll get a message back after some time (hopefully within a day or two) with confirmation and brief instructions on how to login, either using ssh or sftp, and how to get a hold of your account password (not required for login but still required for shell users who run chsh, for example).
Note: You can generate a new SSH keypair by running 'ssh-keygen' and accepting the defaults on whatever host you want to connect from. This will generate a file named 'id_rsa.pub' that is what you send by email. Take care to not send your private keyfile (the one named 'id_rsa' by default), otherwise you'll need to regenerate both keys.
For existing users on the Zaibatsu: We're enforcing a 'no dual-citizenship' policy. You can have a user account on one of the Republic or Zaibatsu but not both. This is to keep things fair - both servers have limited resources and this allows more people to use them. There is less need to even have more than one account since IRC and BBS are shared resources. If you do want to move from Zaibatsu to Republic, the admins will give you time to migrate your data but after some reasonable time period we'll remove your Zaibatsu account (we'll work with you and help you migrate accounts if needed).