Iron golems are 2.9 blocks high and 1.4 blocks wide.
Iron golems will wander around a village in a patrol-like fashion, staying close to the edges of buildings and such. Like villagers, iron golems will not wander away from a village, regardless of how they were spawned. Iron golems will sometimes face a villager, as if they are speaking to each other. Iron golems are able to hold poppies and give them to villagers, symbolizing the friendly relationship between the villagers and golems. However, they won't give poppies to other iron golems.
If not within a village, iron golems will slowly wander aimlessly.
Iron golems can walk up a full block height without jumping and walk over a 1 block wide hole without falling in. They will avoid water and lava at all times, but not fire or cacti. Iron golems are immune to both drowning and fall damage. When in water, they will sink, immobilize, and become passive, but will still be pushed by flowing water.