The Leaderboards can be found by clicking the P symbol at the top of your home tab on iOS and Android.
At a glance you can see 3 rankings: Global, Groups and Contacts.
Your Global Ranking will only show if you are in the top 10,000 and compares you to every Palringo user in the world. Global will not show if you are not in the top 10,000.
Your Groups Ranking compares you against the Palringo users you share a group with.
Your Contacts Ranking is your position among your contacts.
Your ranking is based on your reputation so to increase your ranking simply increase your reputation this can be done in many ways one such way is gaining achievements.