This post isn't meant to be tutorial. It just give you vision that we can implement this feature on static blogspot template. This feature is already implemented on dynamic blogspot template and truthfully this post is also taken inspiration from the autocomplete search from dynamic blogspot template.
So what searching with autocomplete functionality stands for? AFAIK, it's a feature when you type something in the search box, it will provide you auto suggestions that relevance with whatever you type in it. It will provide immediate result without need to click the submit button and redirected to the result page (If you want more clear explanation just try to search something on blog that use dynamic template).
In this post I try to experiment this feature on blog using autocomplete jQuery library made by twitter called typeahead.js.
So to try this feature, I have made following steps: