To include taxonomy pages (categories, tags, custom taxonomies) in the search, enable the option in the options page. There’s also the option to choose which taxonomies are included. By default everything is indexed.
Currently the title of the taxonomy is indexed with the description field. Indexing other fields isn’t currently possible. Taxonomy pages should be automatically updated in the index whenever they are edited.
In the search results template, avoid get_permalink(), as it doesn’t work. the_permalink() works and returns the correct permalink. You can use relevanssi_get_permalink(), if you don’t want to echo the permalink directly.
In the post object created from the taxonomy page, $post->post_title contains the name of the taxonomy, $post->post_content has the description, $post->link has the permalink and $post->post_type will contain the name of the taxonomy.
If you want to modify the post objects Relevanssi creates from the taxonomies, you can use the relevanssi_taxonomy_term_to_post filter.