Register for DMR / NXDN
Thankfully things are a little more simple now for DMR/NXDN registration than they once were. There were a number of registries that were in use for DMR IDs, plus a totally seperate registry for NXDN. These have since been combined and you can now use RadioID.net for all of your DMR/NXDN ID registration needs.
Register yourself for an account at https://www.radioid.net/, once you have your account setup, you can then go through the process of registering for your ID(s). You should only need a single DMR ID and single NXDN ID.
You can check your registration status, either at RadioID.net or here on this website http://www.pistar.uk/dmr_regcheck.php, the tool hosted on this website will indicate your registration status in the DB that is available to all Pi-Star users, you will find that it can lag behind RadioID.net by almost 24h, I offer this lookup because you are able to see when your callsign will show up on the dashboard for all Pi-Star users.
Note: Some D-Star reflectors have required a CCS7 (DMR ID) in the past, even if you only use D-Star, you may also need a DMR ID registered.