So would it be a Kentico user? Or do you want to create a public page where Users can signup?
I'd recommend to store the data in Kentico First and create either a Task or process to send them to an alternative system separately.
Unless you have to confirm or expect feedback directly from that API back to the user.
I'd say start of with the documentation:
Based on your development model you'll move up to either MVC specific:
or into the Portal engine section: