This might seem the simplest of guides, but I've already lost count at the amount of players in game who are unsure how to unlock Masteries. With that in mind, this guide covers not only how to unlock them but which Masteries you should unlock first. 

Overview

Masteries are a new account based progression system that grant access to new skills, utility or areas of the game world. They are split between the core game and the new region: Maguuma Jungle. In simple terms, players complete content and overcome challenges to gain Mastery Points which they can then spend on Masteries of their choosing. You should also note that each Mastery Point tied to a particular objective can only be acquired once per account and only one Mastery Track can be active at a time. Completing a Mastery Track, as noted above, can reward all your account's characters with new abilities, such as:

1. Learning hang gliding to soar through the air instead of falling, or learning to use various mushrooms in the jungle to bounce to higher places, run faster or recharge your skills

2. Learning the languages of the civilizations of the jungle, earning their trust, challenging their champions, unlocking secret locations and learning new combat techniques

3. Unlocking collections for obtaining legendary weapon precursors, with collections for each weapon

4. Unlocking achievements in Fractals of the Mists, fractal challenge modes, more powerful infusions and instance-specific buff items

5. Unlocking Mentoring Badge for your characters and gaining speed boost in cities and bonuses for crafting, reviving and picking up loot

An image of my character currently leveling Upgrade Use on Glider Basics

Leveling Masteries 

While active, completing events, killing enemies or undertaking your personal story in the Maguuma Jungle will grant experience to that Mastery Track. You can see your Mastery Track experience by holding your cursor over the Track, or your experience bar at the bottom of the screen. Undoubtedly the quickest way to maxmize your early Mastery Tracks is via the personal story which is not only fast, but super fun. Just head to the Silver Wastes and follow it into Verdant Brink. 

Finally and because this is a question I've already been asked lots, I'd recommend you upgrade the following first:

1. Glider Basics

2. Bouncing Mushrooms

3. Updraft Use

These three give you direct access to most of the canopy and allow you to reach many of the Hero and Mastery Points. Oh, and be sure to equip as many XP boosters as you can!