Basically Elimination Communication is listening to and following baby's pottying cues and holding baby over a "potty" (whether a child's potty, a "real" potty, or another container of some sort) when it needs to urinate/have bowel movement. Baby has elimination cues just as it has feeding cues....some more pronounced than others

. We "catch" most of Coren's pees/poops (since he was born on Saturday, he's done two partial poops and 4-5 partial pees - he stops when he feels the wetness - in cloth diapers) and what we don't "catch" goes into a cloth diaper, because we DO use cloth diapers (some EC'ers don't use any diapers at all). Some EC full time, some part time (during the day, but not at night for example).
Some links:
Natural Infant HygieneDiaper Free BabySept. 26 Newsweek Article
We have DFB meetings in my area once a month - I actually looked into it a bit before Coren was born because several of my friends practice EC and I found/find it fascinating. I just never thought I'd be doing it FT myself! Now I plan to do it at least PT.
My dd EC'd herself starting at around 9 months when she figured out how to pull her diapers off - and as soon as she could walk (10.5 months) used her big brother's "little potty" or stood in front the big toilet to pee (like her oldest brother! :LOL ). Since I couldn't keep a diaper on her at home, I just watched for her cues and sat her on the potty whenever she seemed to need to go. She was diaper-free by 14 months.