Teamfight Tactics Beta Pass is officially live, bringing rewards specifically related to this mode that are earned through some major grinding. Currently, some functions are still not enabled but should come along sooner rather than later.
Teamfight Tactics seems to be hugely popular as it's constantly on the top of Twitch's top 10 viewed categories. The next natural step for Riot would be to start monetising the game mode but they seem to be holding off on that because it's still in beta, just like the first iteration of what will likely become a Battle Pass in the future.
As a tiny play on words, they named it Beta Pass and it's available to everyone for free. Players can start earning points by completing weekly objectives that are not too hard to finish but quickly run out, before even reaching the first reward. The weekly objectives award 90 points in total while the first reward requires 100, leaving it unobtainable at the time of writing.
The other way of obtaining points needed to progress the Beta Pass is Orb of Enlightenment. It requires you to play at least five games in a day and will then allow you to claim more progress points.
It was still disabled when we checked, with a timer that hints it will go live at some point during 2 June 2019. In this particular case, it will be 18:00 CEST / 16:00 UTC / 9:00 AM PDT. On the other hand, it is basically 24 hours after unlocking the pass.
Reward scaling seems to indicate a lot of grinding will be involved in the process of gathering them. For example, getting the first emote reward at Tier 4 will require 1,000 points while the weekly challenges award only 90.
The scale of grinding largely depends on the daily reward's size. The weekly missions seem to shift after completing each batch with higher rewards each time.
Then again, the last tier with rewards other than Summoner Icons is Tier 7 so it's not really necessary to go full Pokemon trainer mode and catch 'em all.