Giving Page its own Template/ Widgets

Hey ,
What i want to do ? : I want to make a page on my site and add a custom Google search engine . i don’t want anything else on the page except one adsense ad . page would look something like this

https://blogspotblogsearch.blogspot.com/

Problem : the problem is that i am new with wordpress and i am having problems with giving a complete new template to just one page on site named ” search” . i am planning to add a search page somewhat similar to the homepage of Google . (simple and just showing the search box in the centre) . are there any plugins i can use to do this . and if there aren’t any what files in the theme should i edit , ( i don’t want to mess up the whole template )

Thankyou