All prices will be rough estimates based on the largest quantity of "cheap" products i could find (mixed at manufacturer recommendations if need be)
Step 1: Tap Water: $0.003 / gal
When thinking cheap, bottled water is ridiculous. Some people may buy bottled water to use the bottles; I tried to re-use the pop-top arrow head bottles but found they all failed quite fast under normal use. A good, cheap water bottle with a one handed operation is your best bet.
You should drink a good amount of water each day, whether it's in other drinks or foods. Don't worry about numbers, rather learn the signs of dehydration and obey your thirst. Keeping water around you constantly helps hydrate your body because there's less chance of going thirsty because you're too lazy to go get a drink.
Water is great and all but few people want to live on water and food alone, so here are some common drinks available at the supermarket: