Basic Information
The Battle Pass was first introduced on 7/19/18, and it costs 180 Gems. There are 100 tiers to complete, with each tier needing more experience to complete.
There was a battle pass before Season 1, commonly called the Alpha Season, which had only 30 tiers. Some of the cosmetics you could earn from that season are listed here.
Cosmetics from the Battle Pass are exclusive, meaning once the time is up you can no longer obtain the cosmetics listed in the pass.
Free Pass
If you don't want to buy the Battle Pass, there is the Free Pass, which every player gets by default. The rewards are limited, and the last reward for the Free Pass is currently at Tier 50. Keep in mind, buying the full pass for 180 Gems has rewards that go up to tier 100.
Weekly Challenges
In the Battle Pass, you need to level up your season level to obtain stars; upon collecting 10 stars it moves you up a tier.
Leveling your season level up once gives you 5 stars, so you would have to level up twice (level 1 -> 3) to move up 1 tier.
There are four sets of weekly challenges, each set containing 7 individual challenges. Completing ones listed as "Hard" give you 10 stars, effectively ranking you up to the next tier. Each set of challenges total to 50 stars, so completing the set will basically give you 5 tiers.
Daily Challenges
There are 3 daily challenges available every 24 hours. Completing these will give you 20 stars.
Buying Tiers
If you are falling behind and want to catch up, you can spend gems to upgrade your tier.
Doing so will immediately unlock the next tier(s).
XP Boosts
XP Boosts (experience boosts) are unlocked via the Battle Pass, and they help you earn experience towards your season level.
Currently there are 10 total boosts, so you can possibly have a 100% or double XP boost.