How do I promote my lower tier troops?

Open the screen to train your troops (e.g. in the Shooter Camp) and select near the bottom the lower tier of troops. If you have any of the lower tier then you will see a yellow arrow appear in the top left. Tap this to go to the promote option.

As with training you will need resources to promote and then wait for it to complete. Promotion will be to the highest tier you have unlocked. You can only train or promote troops at any one time.