From their telegram:
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✈️✈️✈️ AIRDROP: Welcome EOS holders. We will be announcing more details about the airdrop in the next few weeks. It will be ERC20 so make sure you hold your EOS off exchange when the snapshot date (to be announced) occurs. If you participated in the crowdsale, be sure to claim your tokens beforehand. We will give at least a week's notice ahead of time so you have time to prepare.

We will be releasing the tokens before the June 1 2018 EOS mainnet release. This should help stimulate community growth and engagement, especially because we want token holders to vote for some ground rules of the Everipedia Network.

UPDATE (1/24/2018): Right now we are working on various coding challenges:
1) How to make sure EOS holders are accounted for between now and also after the mainnet launch
2) The airdrop script itself
3) Tracking down the current balances of EOS holders
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I think you need EOS in your wallet and registered.