go to talktomeinkorean.com

it's amazing!

Websites are helpful, but a knowledgeable language partner is best.  Through the internet you can create a virtual classroom environment that will be quite conducive to learning to read a new writing system. A language partner who is somewhat fluent in English will also benefit from teaching you, so don't give up!

I didn't learn to read Korean through the internet but did learn to read Persian with a patient language partner, Skype and Google documents.  Believe me, the Persian writing system is much more complicated than Korean.

For Korean, the first thing to do is to have your language partner show you how the letters go together in a chart like this:

http://www.ksngn.com/news/photo/201408/2373_2628_3140.png

Learn the sounds of certain easy consonant and vowel combinations.  I recommend that you ask your partner to first teach you these consonants: ㄱ, ㄴ, ㄷ, ㅁ, ㅅ, ㅇ and these vowels: ㅏ, ㅣ.

Don't worry about learning the compound vowels or double consonants until later. Oh, and learn to write the letters following a standard sequence of strokes.  This image might help:

for consonants:

 http://static.tumblr.com/flrdsan/Mkrmj16s2/1.png

for vowels: 

http://static.tumblr.com/flrdsan/hXLmj16t0/3.png

Your language partner can show you alternative fonts.  These are too rigid but at least you can learn the stroke order.

At the very least, my response will bump this to the top.

Good luck.

Make sure to learn hangul first! From my experience learning Korean, knowing the characters helps a lot better than romanizaton :)