Problem with Ajax

We are currently developing our website and on a wordpress platform. Ajax is a good thing to use on the search box but my problem is how do i remove the previous searches using ajax search. Do I need to clean the cache every time or do I need to make a new script on it. Sorry if my question is misleading or what, I am just a junior developer and currently I am exploring new trends of coding to finish my project. Please advise if there are things I need to learn or things that I am doing wrong. You're reply is much appreciated.

A) Example if you have one?
B) Are you making a new request on keypress?
C) Remove previous searches?

Are you wanting to learn more about ajax?