I have a dog his name is Milo, Milo knows lots of tricks, and my friends all ask me how to do them, so:
SIT: push your dogs Bottom down so he goes into a sit position ( say "sit as you do ), reward him, repeat this ten times, then don't push his bottom down and just say "sit", if he doesn't listen repeat from the start, if he does reward him with two treats and try again.
LIE DOWN: get your dog too sit, gently take one of his legs ( don't life it up, it isn't "paw" ) see if he's comfterble with you doing so, its best to give him a treat for being good about it. grab the other paw and slowly pull ( be very gentle about this, another way is to push down inbertween his shoulder blades, or on them ) say "lie down" and repeat, ten times and then try it without pushing, or pulling.
PAW: make your dog sit, then take his paw and say "shake" or "paw" or "nice-to-meet-you" or ... you get the picture. repeat until he can do it himself.
STAY+GO: for this you need a command that means "no" for example: OI, AAAAH, >GROWL<, something like that, or even just a yell, get something that your dog wants: ball, bone, treats, food.
get him to stay by saying stay, if he doesn't listen ( which he won't ) then go "OI" or "HEY" ( try to add a growl ) and say stay, this is something that Milo learnt over time we made him wait for his food, or wait to get his ball, or when we buy a new bone ( he really likes bones ) we would say "Milo, Stay" in a gruff voice, and know he knows stay like sit! go when your dog is staying, say go, he shall learn that go means go!