The WP User Manager Likes addon has some functions that can be used in templates to access certain data.
wpumli_get_likes_count( $post_id )
This function will return the number of likes a piece of content has, when supplied with the ID of that post, page or custom post type.
wpumli_get_likes_by_user( $user_id, $post_type = null )
This function will return an array of post IDs for the content a user has liked. You can optionally pass a post type string to only get the likes for a specific post type.
wpumli_get_users_who_liked_post( $post_id )
This function will return an array of user IDs who have like a piece of content.
wpumli_get_liked_posts_for_profile( $user_id, $post_type = null )
This function returns the liked content for a user and is used to render the profile content on the Likes tab. It is pluggable so you can overwrite this function in your own code.