First off, you don't log onto mIRC, but rather, you use mIRC to connect to one or more IRC networks.
Basically there are two kinds of registration.
1) Registration of mIRC. Type /registration then fill in the information in the dialog that will popup.
2) Registration of your nick on an IRC network.
This second one is usually done using /msg nickserv register <password> <e-mail address>
Replace <password> with a password that you won't forget and <e-mail address> with your e-mail address.
Further assistance with the second type of registration should be re-directed to your networks help channel, usually #help
