Register for YSF / P25
P25 users need to register for a DMR ID, the same ID is used for both modes, there is no seperate registration for P25 required.
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.
Yaesu System Fusion, some times called YSF or C4FM (and can also be used with FCS reflectors, just to add to the confusion) does not require any kind of registration, just set your Pi-Star hotspot up with your callsign, and make sure the same callsign is configured in your radio (no hyphen "-" etc.) and that is all there is to it. Yaesu operate a closed network called Wires-X, when using Wires-X a registration IS required, however since Pi-Star is unable to talk directly to Wires-X at this time, I don't believe there is a need to cover that here.