DO NOT DRIVE THE CAR BACK TO THE OIL CHANGE PLACE!!!!!!!!
If most of the oil has leaked out on the way home and at your house then your engine will sieze up with a minute or two of driving it dry! Even turning the engine on and idling it is dangerous.
They really screwed up: undertightened the drain bolt, used a faulty filter (hole or seal is bad) or "double-ringed" the filter (old seal ring stays on the metal rather than on the filter when it is removed and thus interferes with the new seal ring for the new filter).
The oil change place will likely fight you tooth and nail because: "hey, we don't make mistakes here!". Evenso, you might want to call them up and be nice at first but then bitch, bitch, bitch your way into them sending a guy out to re-change your oil at home.
Otherwise, your best bet is to find a guy friend who knows how to change oil and check the plug and replace the filter where the car now sits.