You need to cover the bowl with something like a damp towel to keep it from crusting over. You can then store it in the fridge.
I store mine at room temperature - just on e the counter - in an air tight container.
I place plastic wrap on the surface of the icing. Like you do for pudding. Just press it down and get all of the air out. Then make sure you seal the container. Air is the enemy. You have to rebeat it before use, but I have some that is 3 weeks old. I use it in demos and just rebeat if every time. You can always add water, but can't take it out.
Well, I made Royal Icing for the first time this weekend and I had a problem!
Do you have to wait a while after you make it to use it. I tried to make flowers with it and it seem to just want to run together, it did not look good! 
Please Help! 
Thank you
Connie
It sounds like your icing is just too thin. I would try adding more suger to it. That has always worked for me in the past.
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