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As you probably know, the way to conquer tiles is to set your units on a border, and buy Power.
However, you probably also noticed that Power has a massive waste rate: it starts at 80%. 80% means that even if you have 6 power, it will go all the way back to 1 on the next turn, meaning you will have to buy all of it again. At 10, it goes down to 2. Ouch.

As such, early warfare is extremely costly. Do NOT try to be continuously at war, you will just ruin your kingdom and fall behind.
Here is my advice:

• Do check the balance of Power on the tiles you are trying to conquer/defend. Spending 100% of your money on power is rarely useful, with just 2 or 3 more power than your enemy, you already have a very good chance of winning.
  
• If they are not too expensive, power technologies are better than buying more power if you just need 1 more Power to be safe.
  
• Lay down your sword every once in a while. After you've successfully defended/captured a tile, set your Power spending back to 0% and save some money; money that you should spend on reducing Power waste.
  
• Constant warfare is only tenable once your Power waste is down to 55% or less.

A few other things about Power cost that aren't that obvious:

• Each Power point costs 1 more per unit you have. The base cost is 4£ per point, so if you have 3 units, it will cost 7£ per point.
  
• It actually costs even more! Each additional Power point bought in a turn costs more than the previous one: the second point costs twice as much, the third one thrice as much, etc. This is actually explained when you hover the price.

As such, it is important that you do not buy more Power than what you need.

Also, there is an opportunity that asks you to reduce your Power waste to -50%, and in exchange makes each Power point cost 1 less. I advise to let your waste linger at 55% and wait for that opportunity to appear.

Yes, having a lot of territory means having a lot of resources and thus completing objectives faster; especially since Ozymandias doesn't set any limit on how much territory you can have, unlike some other games.
However, most objectives don't require you to go to war. And remember that cities provide a defensive bonus to nearby tiles, which increases with its population. With big cities near your border, you can easily defend yourself while spending very little on Power, allowing you to spend your money on other things, such as science and food for opportunities like the Zoo or the Palace, that give you crowns, or just saving your money to complete the Hanging Gardens.

If you are going to play a civilization that discourages war, like Ecological or Mercantile ones, remember that you can change how many crowns are necessary to win and how many each wonder gives. You can even set them to zero! If you want to try a pacifist run and make it easier on you, go ahead and disable military wonders.