I'm not sure this works for grapes, but I know the method they use for watermelons is quite clever.

Sex cells, like sperm and eggs, are made by evenly splitting chromosomes. Humans, for instance, have 46 chromosomes in 23 pairs, and each pair splits off so the sex cell has 23 chromosomes. Those 23 mix with the 23 from another person's sex cells and you end up with the 46 chromosomes that will make a new person.

But if you have an uneven number of chromosomes, you can't split them, and will therefore be sterile and incapable of producing sex cells. This is why mules are (generally) infertile - horses and donkeys have different numbers of chromosomes, so while they can reproduce and make a mule, that mule has an odd number of chromosomes and is sterile.

So for watermelons, what they've done is taken a strain and engineered it to have doubled chromosomes. Rather than have 30, for instance (I don't recall the exact number of chromosomes they have but it's not strictly relevant), it has 60, with every chromosome just duplicated. So the genetic makeup is the same and the fruit is exactly the same. They can breed the normal watermelons with other normal watermelons and the doubled watermelons with other doubled watermelons, and either of those results in seeded fruit, which they can use to keep growing the next generation.

But when they cross the two, the resulting melon has an odd number of chromosomes (in the example above it'd have 15 from one parent and 30 from the other for 45 total). It's still got the usual genetic makeup and grows as normal, but as it can't form sex cells, it doesn't develop seeds.