Plugin Dev: How do I code a dynamic form?

I’m looking to add what I think would be a simple form to my plugin.

I would like to be able to dynamically add a field at the user’s request. The user would go to the form and add some information like day/time/etc.., then the last field could be used just once, but could also be used more depending on how many they had to add. Then when they submit the form I could just loop through and put all the info into a db table.

I have all the stuff working with a set number of fields. How do I use jquery or whatever, to add fields on demand then stick the fields into the db?