AceSearch is easily installed as any Joomla component. That should be done through your site's backend.

Once you log in, you should open the Extensions => Install/Unistall section and click on the [Browse..] button in the Upload Package File section. Navigate to the same AceSearch file you have downloaded earlier and select it. Then click on the [Upload File & Install] button to start the installation. It will install :

1. The main AceSearch component
2. Back-end & front-end search modules and quick icons module for back-end
3. Language files
4. Installer adapter that will enable installing AceSearch extensions via standard Joomla installer
5. Database tables (#__ acesearch_extensions, #__ acesearch_filters,  #__ acesearch_search_results)