The concord grape, was first developed by Ephraim Bull about 150 years ago and is a member of the Vitis labrusca family. Growing the concord grape will means growing a robust very recognizable species, with a color palette that ranges from deep purple to dark blue. The Vitris Labrusca family is know as host for many table and wine grape species, the grape has large seeds and is because of it's aroma also used for jelly, juice and other foods that need a typical "grape taste or bite". When you are interested in growing grapes yourself this species may or may not be a good choice.

About Grapes in America

Today more than 400,000 tons of Concord grapes are produced commercially each year. Most of them are not found on the grocery store's produce racks, today we prefer the seedless variety over the large seeded Concord. So when you are looking for a nice grape species to grow at hone the Concord might not be your first choice. That's not to say the home gardener cannot grow this variety if they want to - and can get a cutting. However, it is not necessarily the best kind to grow if you want eating grapes. Still for the serious wine maker it can be a good choice. A good overview of  what can be grown in this country, is the University of Minnesota. They have published an extensive study about the different grapes varieties that are successfully grown here. Although Minnesota is there point of reference, you should have no problem extrapolation to your local conditions.

The first pick

So long as your climatic conditions and soil are both suitable for the Concord grape vine , there should be no difficulty in growing them. When growing, care must be given to establishing the plant over at least three years before grapes are picked for harvest. That's not to say you won't get any grapes at all for three years.

What you should do is pinch off the flowers for the first two years so that strength will be established in the roots. The third year you can leave about half of the flowers to bear, though pinching them all off again is actually better for the plant.
Exercising your patience in this way will see a strong plant established that should last for at least 40 more years.

Like many plants, if you simply grow seeds from a bunch of Concord grapes you bought, they are not likely to be the true variety. They could turn out really bad grapes - or they could be even better than the Concord, but you won't know for some years, so why risk wasting all that time? To get the true variety, you need to buy or beg cuttings, or slips as they are called.

Soil Requirements

All grapes need rich soil with plenty of compost in it. A south-facing slope is an excellent place to grow Concord grapes, but if you just want one or two plants growing around your house, make sure they are sited to get the most sun possible. Weeds and other plants should be kept away from grape vines. This is especially important for the Concord grape for this species is particular prone to Black Leaf. This plant disorder inhibits photosynthesis because the grapes leaf looses it's chlorophyll.
Black Leaf, often thought of as a potassium shortage, is an especially unwanted condition in fruits because photosynthesis is responsible for the transformation of sunlight into sugars. This condition has never occurred in my own practice. From the resources I referenced to get more clarity on the matter the short but concise Wikipedia article on black leaf was the basis for my conclusions. 

Pruning Your Concord Grapes

Grapes should be pruned in late winter, before the sap starts to rise. Fruit is borne on last year's growth; so don't take too much off. But yet, if you don't take enough, the quality of the fruit will be quite poor. When you see the early spring blossoms, make sure you also prune off any weak spindly growth. More vines will grow from the end of the blossom and this should be pruned off at the third or fourth leaf.
Unlike much other fruit, grapes change color well before they are ripe so make sure you examine the size and taste them before you pick. Under-ripe grapes will be sour or tart to taste. Growing the concord grape is not especially difficult, but when you take the possibly problems with this species into consideration it might be a good idea to have a close look at possible other options.