What is the proper way and temperature to store yeast?
The answer varies depending on the type of yeast, but in general, the fridge is a good bet (37-41F). Dry yeast can stay viable for a long time stored at room temperature, but liquid or cultured yeast should definitely be stored in the fridge to keep them in a dormant state and increase their longevity (dry yeast will also last longer in the fridge but it's not strictly necessary). Cultured yeast should be stored in pure, sterile water (you should be able to look up methods of "washing" yeast from previous batches pretty easily), while store bought yeast can be stored in whatever container it comes in.
Store your store bought yeast in the fridge, regardless of format (dry v. liquid).
If I order yeast online with ingredients from a web store I like to make my starter right away. Then I put the whole starter in the fridge after it completely ferments out. Because I never really know how well the shipping trip treated the yeast, I figure if I get it started ASAP it will help revive the healthiest cells that remain. Then the starter with spent wort (or sterile water) on top of it will keep for at least two weeks and its ready to pitch. I like to let it come back to room temp while I brew, then pitch the slurry only.