Although the power in itself does not have real value, it is often used in game as a measurement and to get or stay in an alliance it might be required to increase your power. In the long run it is just a matter of trying to keep increasing all power categories (building, research, troop, hero, wall), and below tips are help all the time, but should especially help you increase power early on.
Keep building all the time. Command Center updates give the most power increase per level, but realize it can be cheaper resource wise and a lot faster (auto complete) time wise to upgrade all other buildings, including multiple instances of Farms, Lumbermills, Quarries and Mineshafts, and Barracks, MASH buildings and Power Plants. Fill up all available slots with buildings and upgrade them when you can.
In general try to make sure you keep research going. On this website I will try to fill in the research requirements and power benefit of all research. The overviews will show power/time ratio, so that you can focus your first efforts on projects that give a large power increase relatively.
Always train troops. Having several Barracks upgraded to a high level can help a lot early on, as it increases your building queue allowing you to train larger batches of troops, especially useful when you are going offline.
Hero power is (initially) mostly from EXP level. If you are willing to spend, there are small packs that give you quite a serious amount of Hero EXP, which will increase your Hero to a higher level.
For the rest Hero EXP can come from most activities in the game. Do not forget to use the Hero stamina to hit the Syndicate targets.
Base Missions are also a source of Hero EXP. There are 4 different Base Missions. The Build and Research Missions do not require extra attention, you basically just get some extra rewards for every building level you upgrade and research level you research. For the Train Missions it is mostly the same, although you might check if there are no troops or traps missions that you have decided not to train yet. Even if you don't need them it might be a good idea to just train enough to complete the mission. The Misc Missions require a bit more attention. Early on you can finish some missions that are difficult to complete later on in the game, you can for example build (and destroy) 10 of each Farms, Lumbermills, Quarries and Mineshafts to complete the corresponding Base Mission, before deciding on your preferred configuration. Also others might be worth checking out as they might contain actions you normally won't do.
Also do not forget about the Hero, Alliance and VIP (if you have them) Missions.
I am not really into the wall defenses, but they do give some power, so if this is important to you, keep building up your wall until it is full.
If you have other quick power tips, please share!
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