First of all ensure that your WordPress version is 3.0 or above. If it is okay then upload Plugin files to your server. There are 2 ways for uploading theme files.
1. WordPress Admin Panel:
Go to Plugins → Add New → Upload
Browse your Plugin's .zip file then click install button.
2. Via FTP:
Connect your server then upload your Plugin files manually to wp-content → plugins
After installing the plugin, activate it from Plugins → Installed Plugins
Find “Advanced Search Widget” plugin and click on Active it.