Anybody here who is running the Google Search from Adsense can you explain how it works? You put the search on your site and then everytime somebody uses it to search your site you get paid? How much are people making with it? Is it just like Adsense ads in the terms I can not use my own search function just like I can't click on my Adsense ads?
You don't get paid for searches, you get paid if someone clicks one of the sponsored search results on that results page.
Yep that holds true for google search too. I am using google search and get paid whenever any person clicks on the sponsored-ads that appear at the top of the result page.
As everyone has said, you only get paid if someone searches and then click on the "sponsored ads" that are displayed on the page. You do make a few extra bucks with it, but the main purpose is to add a bit of functionality to your site, making it easier for your visitors to find the things they are looking for. As an added bonus you can actually see the terms people searched for, so it's a pretty good tool to use to get some new content ideas as well.
A search function is rather important on a big site, yes. You may as well try to get a bit of money for it.
in terms of earning income is concern its no use of having a search bar in your website...against the by clicks in Google's PSA.