Oh haven't you opened a can of worms!
Really though, grapes are one of those things that can be fun and rewarding and one of the biggest headaches ever. Growing up we grew grapes (amongst other things) for production so I got to learn a lot about these wonderful vines.
So, since the Concord grape is one of the most common grapes around and from your description of it's flavor I'm going to assume that this is the grape. That being said, here's a quick run down about them.
Assuming that, Concord grapes have a very low and hanging growing habit. The vines should be trained high to compensate for their low hanging habit. Traditionally, grapes are pruned in the spring and normally 75-85% of the vines are pruned. Yes, I know that sounds drastic but that's the best way to ensure a good crop. The fruit is produce from the last seasons woody growth. If you prune too much then you'll have a small harvest and if you don't prune enough then the quality of the grape is compromised. When pruning new shoots remove any thin or weak look shoots and only leave the strongest ones. Remove any dead or damages wood.
In some situations, a winter pruning could be done but this is not recommend because it can damage the plant if a hard frost hits.
Sun reaching the grapes is crucial for good fruit. That being said you should train the vines horizontally and space them about 12-16 inches apart. This allows for good air circulation and sun to reach all of the plant. As the plant grows you should continue to prune back new shoots, once again only leaving the strongest and best shoots. Keeping your plant well trimmed is very important when trying to get a good crop. When grapes start to appear remove leaves from around the fruits to allow for better sun exposure.
There are probably tons of good books out there about growing grapes. You should really confirm the variety of grape since each one is very unique and that would help you really determine the best pruning methods.
Happy gardening!
