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Copy the livesearch directory as-is in your wp-contents/plugins/ directory (the resulting path should be wp-contents/plugins/livesearch/ ).

Then optionally copy the livesearch/livesearch.css file in your wp-contents/themes/yourtheme/ directory (if you want to have a seperate css file for each theme). This file can be modified to match your theme.

Then enable the plugin from the WordPress plugin administration section, and enjoy!