My home currently has wiring that consists of one Black, one White, and one Bare conductor. I am installing a new cooktop w/a downdraft. It has one Black, one Red, one White, and one Green conductor. The White and Green wire seems to be bonded on the end. How do I wire this?
Assuming you're in the US. If the new cooktop has three conductors, that means it has components that run at both voltages (120V and 240V). Most likely, the heating elements run at 240 and the downdraft fan runs at 120.
Your existing circuit, because it has only black and white conductors, is wired for either 240V or 120V. You cannot power your new cooktop from this existing circuit, so you will need to install a new circuit breaker and run a new cable.
You should also identify what the cooktop requires in terms of current. It will need to be served from an appropriately sized double-pole circuit breaker using appropriately sized wire. Building code may also impose minimum requirements for service to an electric cooktop in excess of the manufacturer's requirements, so check with your local building authority if you're uncertain.
Finally, the bonding of white and green wires in the cooktop is not advisable (edit: and per comments below
is not allowed edit 2: may be allowed for replacement appliances installed on previously compliant circuits). This may be an option the manufacturer recommends when a proper ground is not available, but shouldn't be applicable in your situation as your new circuit will carry a ground (bare) wire.