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
do note, registering mIRC costs money (though not alot) and supports khaled in making mIRC. you are NOT forced to register for mIRC and can use it for longer then that 30 day trial period if you want to without concequences.
registering your nickname at a network isn't supported by all networks (but most do), some use nickserv for that, some use other systems. this is usually free.