Not long at all - 'til it gets the 'rise'! by: Matt - Pasta Recipes Made Easy
Hi Pal - good questions sir.
When cooking fresh pasta, it takes just a couple of mins.
Get your salted water really boiling, drop in your pasta, wait 'til it rises to the surface and then it's ready... though I just give it 30 secs more (that's up to you!).
(The only exception to this 'rising to the surface' are orecchiette, which generally don't, so just give them 2 mins then taste.)
As for the drying you mention, yes it's ideal to give your shapes or lasagne sheets a few minutes to stand, as this gets rid of some of the remaining moisture inside. However if you're in a rush, don't worry about it, I don't.
