When you first open mIRC,
the Options menu pops up.
Before you connect to a server,
fill in the Nickname
and Alternative boxes:
nickname1 and nickname2
(or whatever)
must already
be registered

Select Options under Connect,
then click the Perform button.

Check the Enable perform on connect box, then replace the Perform commands with:
/nickserv identify nickname1 <password>
/nickserv identify nickname2 <password>

its ok if nickname2 isn't registered yet,
it will be later, click OK

Reselect Connect under Category
and click the server Connect button.
Join #<channel> like you normally would.
The main nick nickname1
should identify automatically now.

Change your nick to the Alternate:
/nick nickname2
then register it:

/nickserv register <password> <email>

Make the password and the email
be the same as the main nick.
Paste the registration verification code
from the email sent to you re: nickname2
into the channel.

Change your nick back to nickname1:
/nick nickname1
/nickserv link add