Gems in Clash of Clans are the premium currency of the game, something you can use to speed up the completion of almost anything, completely complete buildings, or buy all kinds of good stuff in the store to help you run your village. They also help recruit more builders for your village which means you can get more work in your village while you go about your day.
They can be purchased for real money in the store, but there are actually plenty of ways to earn gems without paying a dime. They'll all need a bit of work, but nothing that gets you too far.
Here are ways to get free gems in Clash of Clans
Achievements
The first and easiest method is to complete in-game achievements, which grant both XP and gems with each achievement. There are also three levels for each achievement, meaning that each will earn you gems to use.
The reason this is easy is that most of the achievements will come from just playing the game. Upgrade to bigger and better buildings, complete single player missions, remove obstacles, unlock certain troops, steal a certain amount gold and elixir to other players are just a few of the ways to do this. You can find what you can do and unlock gems for everyone on your profile page and by scrolling down. If you are patient with using gems, you will earn more than enough from this alone to eventually add that fifth villager.
Remove obstacles
As mentioned above, removing obstacles is just one of the achievements that you can work on to earn gems through achievements. But obstacles are also