temperary save user inputs with jQuery

temperary save user inputs with jQuery

I really don't know how to start with this with jQuery but here is what i want to accomplish. 
I have some user input fields in a form

Name
Firstname
Address
City
"Add button"
"Finish button"


and i have a table underneath these input fields that contains (Name, Firstname, Address, City, remove button)

I want whenever you fill in this form and you click on add that the content of this form is stored into the table underneath the form.  You can add as many lines as you want to that table through the form but if you have made a mistake you could remove this line with the remove button in the table.

When you click the "Finish button" all of the content have to be putted into a MYSQL table with Ajax and PHP. 

I have made this with PHP only and it works fine but every time i add into the table my page have to reload. But how can i accomplish that with JQuery? I have allready take a good look onto the internet but i really did not found what i am looking for. 

My Javascript and jQuery experience is not so very good i mostly do everything in PHP where i am much better in. 

Could anyone help me on the way?

Thanks!
P.