To bring up the character editor, select Edit from the right-click menu on a character portrait in the list of characters in the Characters tab at the top of the EpicTable window, on a character token on a map, or on a portrait in the "portrait bar", the region that's by default just above the central map and tabletops area. Once you hit the Save button, your changes will be saved to disk, and if it's a shared character, other participants notified of the changes.