To have any benefit from this attempt of a simple bouncer-setup guide you must already have access to a bouncer. If you don't you can probably get some advice from those of your friends who already use a bouncer, and might even be able to give you one for free. The 3 steps below does not target any specific bouncer software, and should work just fine with psyBNC and sBNC, the two most common choices at the time I wrote this.

/server -a address.of.bouncer.com -p port -g Bouncer -w password

Replace address.of.bouncer.com, port and password with the actual values.
This will add a server group in mIRC called Bouncer which uses given address when connecting.

/identd on username
/emailaddr username@

Replace username with the actual username for your account.
The @ behind the second username is not a typo.

/server Bouncer

The command above will connect you to a server in the Bouncer group which we added previously.
You will not have to type the other commands in the future, as mIRC will save the bouncer between sessions.