Too start, ask them were they were born. If they were born outside of the US, ask them if they became a citizen or if they are a resident alien. If they are a resident aliens, ask them to show you their resident alien card.
During this 2 minute drill, you should be able to figure out if the guys lying. If he's lying, you probable have an illegal alien infornt of you.
If he asks why you want to know, let him know that you don't hire illegal aliens and you want to make sure he's legally here. If he's legally here, he'll produce.
Right along with you though for stiff penalties for businesses. They can screen based on SSNs etc.