You can either use it immediately as a base for soup, or you can let it cool and keep it for later. If you let it cool and store it in the fridge, it will last a few days. If it sets to a jelly, this is a sign of a REALLY good stock - it's the gelatin that's been extracted from the bones.
I don't bother skimming any fat off - we like fat here
I usually freeze it in "portions" in plastic containers, to pull out and throw into soup whever I fancy making some.