How to promote soldiers?

You can promote soldiers in the Command Center Building. This building will have a number on the front which is your total troop count. Select the Troops option and then find the troops that you want to promote.

You will also need to have completed research to unlock the promote option. In research under the Basic Combat section you will find several research items to let you promote certain level troops of each kind to the max level that you have unlocked. Complete all the research here to unlock all the promotion options.