How to promote units?

This is done in the Military University building. Tap it and select the 'Troops' option. Tap any low level troops you have and look for the promote icon. this is the 3 chevrons. You need to have unlocked the higher tier of troops for you to see the option to promote up to it.

Your ability to promote troops from certain levels will also depend on the research items you have done under basic combat. If you have not done this research then you cannot promote them. The ability to enhance them also needs to be unlocked for each troop type in the troops type research tree.