You can dig them anytime (after blooming). If you dig early, you'll get small potatoes, but if you wait until all of the plant has turned brown and died, you'll get bigger potatoes.

I think most people wait until the plant has turned brown and died before digging.

I'll piggy back onto your question with one of my own in a similar vein..... Once the plants have died, should I dig up the potatoes and store them or should I "store them" in the gound and dig them up in a few weeks/months? Is there an advantage to keeping them in the ground? Is there an advantage in pulling them out now and putting them down in the celler where it's cooler?

Thanks!
Bart

Here is a page with some helpfull info.

John
http://www.countrysidemag.com/issues/89/89-5/Gail_Reynolds.html

Here is a link that might be useful: Johns Journal