Siad is a command we use when we want dog to sit down. You can say it only to a dog, not to human.
There is no word like 'siadcie' in Polish. There's a word - 'siądźcie' and you can say it to a group of people (not to one person), and I think that it's little more polite than 'siadajcie'
These words are also the imperative forms of siadać
We tell two or more dogs to sit 'siad', too
and infinitive of siad is "siadać"
"Siad' is also a noun. When we use word 'siad' while talking about people it means that they are sitting (especially on the floor) in a special way (for example on a PE lessons) I send you a link of the photo.
Grammatically siad is noun used here as command. You also use siad when commanding two dogs (or people to sit), it's just a state you order somebody to take; plural of siad is probably siady, but I'm not sure if this noun has plural (it should have, I don't have Polish dictionary by me), nonetheless it's rarely used in even non-order contexts.
Noun siad needn't be used as direct order, it can also mean simple sitting pose used on PE, check http://sjp.pwn.pl/lista.php?co=siad if you understand Polish for different sitting poses. It mustn't be used outside of gymnastics context, for taking a sitting pose in daily context spoczęcie (from v. spoczywać, resting) should do.
Of course it's not only way, but it's generally accepted; you can teach your dog to roll on 'siad' command for example!
I know other order for dog to lie, leżeć (lit. lie down; in infinitive). It's quite funny that we use infinitive as very direct imperative mood (imperative of leżeć is leż, but nobody uses it when ordering a dog).