MijoSearch 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 => Extension Manager page and click on the [Browse..] button in the Upload Package File section. Navigate to the same MijoSearch 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 MijoSearch 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 MijoSearch extensions via standard Joomla installer
5. Database tables (#__mijosearch_extensions, #__mijosearch_filters, #__mijosearch_search_results)