This is an example on how to save data in sheet using google script;

HOW TO DO:

you need to create a new sheet in google drive,
add headers in first row
go to Tools => Script Editor => New Script
copy code from google_code.gs and past it
go to run => Run function => select setup
go to Publish => Deploy as web app, for: Who has access to the app select Anyone, even anonymous;
copy Current Wep app URL
past it to you index.html where you have ajax request to send;

keep in mind: For form that you have, You need to have the same fields names as in sheet;