Where do I find my bill and set a spending budget in the AWS console?

I created an AWS free tier account to experiment with a small project, and I've heard horror stories about surprise bills. I want to check what I'm being charged and set up an alert before spending any real money.

Directions to the billing section of the AWS console and how to create a budget or billing alarm.

The AWS console home shows dozens of services and a search bar, but I can't find anything obviously called 'billing'. I found something called Cost Explorer but it wanted to enable itself first, and I'm not sure if that's the same as setting a budget.