The first thing to do is to select an appropriate container made for holding food items. This could be a glass, stainless steel and polyethylene plastic containers/bottles/ jugs.
Before storing the water make sure that the container is thoroughly cleaned. Inspect the container yourself just to be sure.
It is extremely important to boil the water before storing it. So bring it to a rolling boil in order to kill all the bacteria in it.
You can also choose to use chlorine in order to purify your water which is about to be stored. Remember to use only 16 drops of unscented chlorine per gallon of water.
Now after pouring the water in the container/ jar, seal it tightly (almost air locking it) and place it in dark, shadowy areas, away from sunlight.
Keep the containers away from gasoline, kerosene and pesticides, as their vapours can penetrate the plastic body of the container if it is thin enough.
Also make sure that the area is not very damp as it can cause fungus to grow inside the container if not sealed tight enough.
If you are travelling and need to move the water with you then obviously carrying huge containers is not an option, for which you can buy travelling bottles and keep them in your luggage.