Where in the Constitution does it give congress the authority to regulate the rights of the American citizens?

The same place that gives congress the right to create a massive welfare state...the same place that gives them the right to regulate your thermostat in the name of their false religion global warming....the same place that gives them the right to reward bad behavior and punish just behavior...the same place that gives them the right to put a GPS in your car so they can tax you per mile and be able to see where you are, how fast you got there, again all in the name of their false religion global warming, and to give them the ability of seeing who you are associating with and violating our true right of privacy............by now I hope you realize that there is NO PLACE IN THE CONSTITUTION FOR ANY OF THESE I JUST MENTIONED!!!....yet they are all being presented by our government at this time...and those of use who believe in our true Constitutional rights are being labeled as "right wing extremist"....which is why I proudly call myself a right winger....this is why I will fight for the greatest country God ever gave man...it would be a sin to just sit by and do nothing while unbelieving people work to dismantle that which was given by God....yet so many do just sit by and yawn...what a shameful lot this country is turing in to....if our founding fathers were alive today, they would have had a second revolution by now..way before Obama got in to office....

It depends. Your question is a very broad one - an example would have been helpful. But here goes anyway.

Certain powers are given to Congress by the constitution. It can legislate in relation to those powers. So, for example, the constitution says Congress has the power "To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes"

So, for example, if you felt it was your right to buy cognac from France, then the constitution does indeed give Congress the authority to regulate that right.

It doesn't. Your rights are defined in the Constitution, not by Congress. And, for those rights that are not specifically defines in the Constitution, there is the "catch all" amendment:

Amendment 9 - Construction of Constitution..

The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.

Basically, this means that the people have rights that are not defined in the Constitution. What those rights are are pretty much up to the courts to decide, though, not Congress.

For example: The right to privacy is not mentioned anywhere in the Constitution, but there have been numerous court cases that dealt with it.

That's a pretty broad question. What rights are you talking about?