Season Pass is divided into two tracks where you can manually claim additional rewards. The track on the left offers free Pass rewards, while the one on the right offers paid Pass rewards.
You can check the remaining time by entering the Season Pass menu, and the timer will be visible on top of the screen.
Progressing the Season Pass is quite straightforward. Pass levels to unlock more tiers. The more tiers are unlocked, the more rewards you can claim. Neat!