Iron Golems will spawn naturally in any village that has over 10 villagers and over 21 doors. There is also a light requirement, but unless you have an underground village, this shouldn't be worth worrying about. Currently, there are 2 ways to create Iron Golems without cheating.
Build An Iron Golem
So the first and most simple way is to build an iron golem by hand. You can create one by getting 4 iron blocks in a T shape and placing a pumpkin on top for the head. As soon as you place the pumpkin it will turn into a living iron golem. It is best to do this at a village though as they tend to run away when they are left out in the open when there is no village nearby.
Expand An NPC Village
NPC villages will spawn iron golems naturally. If there are over 10 villagers and 21 doors they will begin to spawn. The more villagers and doors your village has, the more golems will spawn. You can speed it up by building them yourself of course. If you are unsure on how to manage a village, this guide will show you how to get more villagers in a Minecraft village.