Potato plant in full flower beside my other assistant (she was complaining that her sister was hogging all the blogging limelight).
Potatoes plants normally start to form tubers, ie. potatoes, when they start to flower. You want to wait until they are well in flower before rooting around for the intermision crop. (Apparently, some varities will not flower or flower late so the above does not apply. The authorities that told me that said to wait about 65 days and then to check for new potatoes... I have no experience so good luck! I grew Carlton and they flowered just as expected, a lovely flush pink).
Another good tip, is that new potatoes are often ready at the same time as ripe peas. Many recipes call for using both. This will depend of course on your varities (use early varities for new potatoes), and climate and - insert usual gardening qualification*.
Harvesting New Potatoes
The best way is probably to plant your early season potatoes in mulch such as straw to make rooting around for the little guys as simple as lifting the straw. I like to do things the hard way so I just yank up several plants. This of course means that I sacrifice quantity later on.
Potato plant with some good sized new potatoes and several very small potatoes still developing.
* Usual Gardening Qualification: Climate, Zone, Variety, Weather Fluctuations including rain, heat or growing index, Soil type and Quality, Pest Prevelance, Weeding Vigilance, Pet Damage, Forgetting to plant on time, Spilling beer on crop (not sure how this would affect it, we should do a trial), Children's Feet or Soccer Balls, How you speak to your plants, and so on.
Agriculural Pictures of a maincrop potato harvest
Fun site on growing potatoes