Disclaimer: I've been reading about EC in preparation for my son's birth, but I haven't tried it myself. Since nobody else has answered the question, I'll try to summarize what I've read for you. Hopefully others with more practical experience will chime in later.
The basic idea of EC is that babies are aware of what's going on in their body and can communicate that information. Think about hunger: babies don't go from "completely content" to "screaming with hunger" right away. There are intermediate stages where the child might start sucking on a fist or acting a bit fussy. The particular signs vary by child, but a caregiver can usually pick up the signs and offer the breast/bottle before the baby reaches the screaming stage. Timing can help as well; if you know the baby usually gets hungry every X hours, you'll start looking for the signals when close to X hours have passed since the last feeding.
EC extends this idea to elimination: it suggests that babies can tell when their bladder or bowels are starting to get full and will indicate this somehow. If you notice the signs, you can offer a potty. Timing can help here too to the extent that babies often go at the same time of day, e.g. after a feeding. Note that the baby's signals will change over time as the baby gets older and can communicate more easily. People who are interested in baby sign language can use it to give the baby another way to signal, making EC easier.
As for the "particular squat position", there's no one position. Young babies will need to be held over the potty somehow, while older children need less or no support. For children that need to be held, there are a variety of different positions described in EC books and websites that you can try; not all children like all positions. The position might also vary depending on the toilet itself. If you want to use an adult-sized public toilet when you're out of the house, you might need a different approach than if you're at home using a miniature potty.
I liked the book "The Diaper-Free Baby" by Christine Gross-Loh if you want to learn more. Googling will also lead you to a ton of useful websites and forums like this one.