Ah, emo music... the world wouldn't be the same without it! Read the following steps to learn how to appreciate and love emo music.

[edit] Steps

Understand what Emo music. Emo stands for Emotive Hardcore (not for "Emotional") a sub-genre from Hardcore Punk, which started in 1985 and died in the mids 90's. Emo songs generally have fast tempos, screaming voices and guitars and deep lyrics. Also, the words Emotive hardcore is often abbreviated with the word EmoCore ("Emo" from Emotive, and "Core" from hardCore)
Listen to Emo bands. These are not usually played on mainstream rock or alternative radio stations, and they are not played on TV channels.
Build your music collection. Check out your local independent CD store, go on PureVolume/iTunes, or just download your selected emo songs onto your iPod/MP3.
Research the lyrics online to gain appreciation for this beautiful, insightful music. Don't let this stop you from having your own interpretation, though.
Go on MySpace or some other music browsing site and browse under the "emo" category and see what happens. Music Store already has an built in emo category, and MySpace has emo, and screamo.
See if there are any emo bands playing a show near you. Don't forget about the local bands.

[edit] Tips

Keep an open mind to all types of music, don't limit yourself.
Do not fall for stereotypes; Emo music isn't about being "depressed" or "suicidal".
Once you find some bands that you like, go to their shows. You'll be able to meet other fans and discover new bands through them too.
If this type of music isn't your thing, don't force it. You may develop an appreciation for it in the future.
Emo songs are not the typical songs that says things like "Oh my life sucks! I think I'm gonna kill myself! or "Oh I can't stand the pain! I'm gonna cut myself!. Emo songs talk about confusion, violence, disorder, disorientation and hate.