To become eligible for Seasons, you'll first need to become a Specialist by reaching Tier 4. Once you've reached Tier 4, qualify for the Season reward by winning 3 battles, and when the season ends you'll be able to collect your reward.
Keep track of your Seasons progress in the Progress menu, which you can access by tapping the Trophy icon on the main menu, which is highlighted in green below.
Keep winning your battles and earning Trophies to move up the Tiers and get a better reward at the end of the season!
There are three additional Prestige Tiers starting at Master, Tier 8. At the end of the Season any additional Trophies earned in these Tiers are converted into Prestige Points, a permanent score for your profile. Your Trophy count is then reset back to 4000 when the next Season begins.