You'll find your Mempal Leaderboard next to the Home icon at the bottom of the dashboard. You can switch between your 'Weekly', 'Monthly' and 'All time' points by tapping on the 'Week' icon.
The Course Leaderboard is the one that appears after every learning and reviewing session - it shows you everyone learning the course on Memrise. To access it, tap on the course title in the top-middle of the dashboard.
Please note: At the moment you can't add new friends (or 'Mempals' as we call them) in the App. However, you connect with them on the website. From then on you can keep track of your friends' scores in the App's Leaderboards!
Related articles: How to add mempals in the website? How does the Leaderboard work in the website? Learning and Reviewing in the iOS App