How do I earn Overwatch League tokens?

Solution 1:

1. Buy them - you already know it, but for the sake of completeness - Shop Page
2. Watch Overwatch League on Twitch. Also, some conditions need to be met (from this support article):

1. Make sure you've set up and linked your accounts correctly.
2. Disable any ad blockers while watching.
3. Google Chrome has a power saving feature which will pause a broadcast if you mute the tab and navigate to a different tab—this will prevent you from earning tokens.
4. If watching on Twitch, make sure your Twitch profile in the upper-right corner says you're watching Overwatch League.
5. Your Blizzard account must be associated with one of the participating countries

3. Signing up to receive updates via email from Overwatch League website grants 100 one time. (source)