Check the yeast and fermenting section... lots of info there.
There are basically two ways to gather yeast... make a starter (out of fresh yeast), step it up a couple times to multiply the cell count, split that, keep some for later, and use some now. This way is always fresh (no trub).
Or
Gather yeast off the cake, wash it, step it up, and pitch. This way you are always dealing with trub, and never really know how much live, viable yeast you have.
As for storing... that's a different subject.