I've grown several other trees from seeds, but never walnuts. As Rosalind says, don't expect anything to happen anytime real soon, neither in terms of nuts or timber

And be aware that if you want them for nuts, cultivars do not come true from seed (normally they are propagated by grafting).
From what I remember, confirmed by google

, they are a deep taprooted species. Trees like that, you're generally best off planting them directly in the soil where you want them to grow (you have to prepare it first and keep the area right around the planted nuts free of weeds and protected from drying out, if you want any meaningful % germination). If you have squirrels, expect significant losses of what you planted out
If you are just going to try a couple rather than a plantation, or if you are *really* worried about pregermination losses to squirrels, you could try starting them instead in deepish pots, ideally sunk in the soil in a nursery area outside. As soon as you have a few leaves up, GENTLY transplant them to their permanent location, with suitable shading for the first week or so. I've done this with taprooted oaks and it's worked fine, but you do need to keep a close eye on things and transplant *gently*.
Also I am pretty positive that this is one of the many plants that needs a cold period before the seed will germinate - if you collected your nuts last fall, make sure to store them somewhere cold but not let them dry out especially if the husks are off, until you plant them.
Wherever you start them, remember they will need *regular* watering and WEEDING AROUND for the first year or three. The weeding thing is especially an issue if you are planting them somewhere with lots of grasses, as opposed to in a forest -- with very few exceptions tree seedlings do quite poorly in competition with grasses until they are surprisingly more well-grown than you might expect.
A quick google finds some useful documents, such as
www.extension.umn.edu/distribution/naturalresources/DD0505.html+planting+walnuts+seed&hl=en&ct=clnk&cd=2&gl=ca
http://grow.ars-informatica.ca/plant.php?en=628&nm=walnut, English
http://www.ibiblio.org/pfaf/cgi-bin/arr_html?Juglans+regia+fallax
Good luck,
Pat