When the ThanksCoin registration is completed you will get the Ethereum wallet-contract. Trough this wallet-contract you may perform all thanks operations.

How to recieve Thanks.

To receive thanks, post your Thanks-button link in your post on Facebook, for instance. To do it, just go to the Account menu, choose the group that corresponds to the content of your post, or use the General group, and copy the link. Insert this button link into your post on Facebook and publish it.

How to send Thanks).

To send thanks, click the Thanks- button or Thanks-link. In general, the users see the Thanks-link in the posts on Facebook in the following way:
for example, Thanks-link of Viktoreum user in the Ethereum group - https: //thankscoin.org/0089aad61d4672c9a0776b7cea4e8ad5a5809b82/564ccaf7, where 0089aad61d4672c9a0776b7cea4e8ad5a5809b82 – is a contract number, 564ccaf7 – is an Ethereum group number. After clicking the link, a new window containing a Thanks-button, will be opened.
If you are using a computer or a laptop and you have installed the Chrome web-browser extension, you will see the Thanks-button instead of the link in your posts on Facebook - 
Click the Thanks-button to send thanks to the author of the post (blogger).
In this case, you should have a sufficient amount of Ether on your account. The cost of one Thanks is indicated in Ethers in the Account menu.

You can find more info on https://www.cryptocompare.com/mining/guides/how-to-buy-ethereum/

In general meaning Group is a virtual social structure.