“Catch up on the story of the dragon cycle and prepare for Guild Wars 2: End of Dragons. Log in to Guild Wars 2 between June 1 and June 7 to unlock these spotlight episodes for free! Check your in-game mailbox for a letter containing story unlock tokens. […] New achievements for the episodes are available in the Bonus Events category of your achievements tab. You can complete these at any time to progress the Seasons of the Dragons meta-achievement and work toward earning legendary rewards. In addition to the new meta-achievement, there are plenty of existing achievements to earn, rewards to collect, and secrets to find in the episodes themselves. Here are some handy links to our official wiki to get you started.”
ArenaNet says to “check your in-game mailbox for a letter containing story unlock tokens,” but I will note that last week’s never arrived for my families’ newer accounts; we had to navigate to the story journal and click the “buy” button on the right episode to buy the episodes for 0 gems. Try both if it’s not working! And yes, you can claim these even with a free-to-play GW2 account.