Companions are promoted within the “My Companion” screen. Promoting a Companion is not the same thing as Training them: Promoting a Companion does a lot towards making them a more powerful team mate.
If a Companion can be promoted – which usually happens when they reach certain levels—you’ll see a yellow exclamation mark in the upper left corner of their portrait in Companion Management, indicating that they want to talk to you.
When you see that a Companion is ready to talk to you about a Promotion, head to the nearest tavern and go down to the cellar where you can see all your Companions standing around. Speak to your Companion to begin their promotion quest.
Once you complete the quest, return to any tavern cellar to talk to the Companion again and they’ll be promoted. Upon promotion, they’ll look different, and they may also be eligible to learn new Epic Powers or Talents.
To teach them, open the Companion Management screen again and click on the New Power button (in the same location as the Train button) – a list of new Epic Talents and Powers that you can choose from will appear.
An Epic Talent is a talent that does more than just increase a stat. But they are still used automatically by the Companion. Bonnie Anne’s Return Fire is a good example– she’ll try to use it automatically whenever she’s fired upon (but won’t always succeed), getting a 'free' attack if it does succeed.
Powers are special abilities that can be triggered while in combat. Once you select the Companion in combat, up to 7 Powers that they know will be randomly selected and displayed at screen bottom. You can tell them which Power to use and who to target. Using a Power uses up that Companion’s turn; A Companion can’t do a normal attack (or move) and use a Power, in the same round.
Move your cursor over the list to see a brief description of each one, and then click on the one you want. If you see a Talent or Power that you already have trained, but it has a number in parenthesis after the name, this indicates a more powerful version that you can learn.