Completed characters are automatically shared between the DCS and the TCG. It's important that you take your character all the way through character creation in the TCG. This means that you need to make it all the way to the character sheet page. You'll see the location where you printable character sheet is located (see the green circle below), and you then need to click the close button. This will take you back to the TCG's main screen. Your character has been automatically saved for you.
Go ahead and close the TCG. The open up the DCS. It's really important that you log in with the same account name and password as you did in the TCG. You will then be taken to the character selection screen where you should see your character.
But what if I still don't see the character?
In this case, please make sure that you've completely exited the TCG. If you have Irridium Cloud membership, your characters are also automatically uploaded into the cloud for safe keeping. Sometimes, the process of synchronizing your character can temporarily make it seem unavailable to the DCS. In that case, open up the TCG again, log in and let it synchronize. Then exit the TCG, and open up the DCS. If you've completed your character in the TCG, you will see it in the DCS.