There are multiple ways to increase your Power value in Civilization War:
1. Train Soldiers
(more on troop stats in this article)
2. Level-up Lord and Greatmen
3. Construct, level-up and upgrade Buildings
4. Decorate Buildings with Emblems
5. Produce Traps
6. Excavate and restore Relics
7. Obtain and store Gems in Jewelry Museum
8. Do Research in the Academy
The higher the level of the action you are performing, the more power value you can get as a result of it.
You can access your detailed Power information screen by tapping on the Power value at the top left corner of the screen, or by tapping Lord avatarDetailed Lord Information.
It will appear in a scroll-list on the right side of the screen, like below: