Storing water
For those planning to remain at home, there's a product called the waterbob which makes it easier to safely store drinking water in a bathtub. You have to fill it while the water is still on, of course, but people often have hours or even days of notice when an event likely to interrupt their water supply is likely to happen.
Rain catchment water is safe for hygiene purposes in many types of emergency. Water from a hot water heater can also be used for hygiene, and can sometimes be safe to drink depending on how gross your hot water heater is. It can be helpful to have a camping shower on hand if you expect to lose water pressure and still want to be able to bathe. Water for bathing can be heated on any fire that you'd cook on, and shelf-stable packaged foods like curries, precooked rice, and even canned goods can be warmed quite quickly by dropping them into a pot of hot water.
Water needs for hygiene can be reduced by:
It would be good to have some pedialyte or other electrolytes to help you re-hydrate.
Liquid rehydration solutions are bulky to store. Search for "oral rehydration salts" in your online marketplace of choice, and you'll find single-serving packets that last basically forever and can be mixed with a specified amount of water. This is easier to store and carry, as you can mix them with water that you get from anywhere. They're great for recovering more rapidly from hangovers and food poisoning even without a disaster, as well.
filters
In the prepper community, the Sawyer Mini is an extremely popular portable water filter. The 2 issues with it are that it can't filter huge amounts of water in a hurry, and if you allow it to freeze after it's gotten wet, the filtration tubes inside will break. The latter can be addressed by storing it in a pocket near your body if you're traveling in freezing conditions with it.
Overview
This guide goes into details on storing and purifying water. This is meant to give you a tool to reason about how to prepare for and act in emergencies that disrupt your water supply.
Storing Water
How much to store?
What do I store water in?
How else do I stay hydrated?
Purifying Water
Boiling
Chlorination
Distillation
Water Purification Tablets
Pump or Gravity Filters
Solar Still