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.
Hope that's helpful, cheers 'Pal' (ouch)
Matt ;-)
PS: Still on the subject of fresh pasta, you might like my new pasta cookbook, as this includes printable versions of my fresh pasta making guides and exclusive downloadable videos of the same.