First note that you'll need either geo-mashup or WP Geo installed in order for Nice Map to be of any use: it depends on existing geotagged data.
Upload the folder nicemap to the /wp-content/plugins/ directory or by installing it via Wordpress's automatic installation method.
Activate the plugin through the 'Plugins' menu in WordPress
Edit the plugin settings and choose at least one WMS layer and one compatibility driver (WP-Geo or geo-mashup, currently) is selected, so that a map is displayed on posts. You should also edit the positioning of maps on posts if you want them automatically added.