The iron golem farm is made to be completely afk so that you can sit back and relax as you watch iron golems burn. It can be a bit slow at the start, but to fix that you can change the difficulty to hard and the iron golems will spawn more frequently.

Another way is to build the iron golem a bit farther away from the village, because the golems can spawn in the village instead. If there is already a iron golem in the village you should try and kill so the villagers wont feel like the iron golem will help them.

This build is pretty big, but this will help in the long run so you will never need to go mine for iron, instead you can just afk near by somewhere.