Hello,
I am finishing my basement and I need to install about 4 vents for Heating and a/c.
The ductwork for the rest of the house is still exposed. I was wondering if there was a special way to tap into the ducts to run these vents throughout my basement (which is only about 600 sqft). If not what's is the best way to do this?
Thanks in advance.

Not really a special a way to tap the existing duct except you just need to use standard HVAC style parts and have the proper tools.

I have found that most home owners like to use insulated flex duct since all you need to do is cut a hole in the original rectangular supply and install a start collar. Then snake it around as best as possible to the location you choose and install a drywall boot and finish the job by joining the flex to that boot.

Try to use a mastic and adjustable (panduit type) strap tightened securely.

You can also use round sheetmetal duct but it will make the job a bit harder to do.

Thanks a lot.
Is there something out there that I could use to shut off circulation to the basement when not in use? Like a baffle or something?

Yes install dampers or close register grills.