I'd bet money that when you told your friends you were moving to Mexico, at least one person said, “Don’t drink the water!” And with good reason. You really don’t want to be drinking water right out of the tap unless you have a filtration system installed.
Instead, you’re going to buy a garrafón, a giant plastic water bottle filled with disinfected water. There are several different companies that will deliver water to your house, such as Santorini, Bonafont, and Ciel.
To set up service, when you hear a guy yelling, e.g.,"Santorini! Santorini!", run outside and tell him that you would like to buy water. How easy is that?! (Yes, you can also call them on the phone, but that’s not near as much fun.)
The first time you purchase water you will also be paying for the garrafones. Once you've bought water from that particular company once or twice, they will usually stop by your house regularly to see if you need more. When they come back, you'll simply exchange your empty bottles for full ones and pay only for the water.
I've never spoken English to any of these folks but as long as you know your numbers (for the cost) and days of the week (in case they ask when they should come back), you should be fine. And don’t forget to tip!
You might want to buy a ceramic container (sometimes accompanied by a metal stand) for easy dispensing. You can find these at stores that sell talavera tiles. However, if you are pinched for pesos, you can always buy a very inexpensive plastic hand pump or a rechargeable electric pump that comes with a USB cord.