I too have had grapes from my vine, and tried the wine-making on several occasions.
It worked once, and did produce a very nice (for home-made!) wine. However, it has failed many more times. The problem is the 'nasty' organisms you get in with the grapes. These multiply during the fermentation, and overwhelm the 'good' yeast. You just end up with vinegar.
You have to be scrupulous about cleaning them before you start. Get all the stalks/leaves off. I'd advise you crush them, maybe even liquidise, and then try to get all the pips out. Sterilise the juice with Campden tablets before you start the fermentation (kills all the bugs).
Add proper wine yeast. Do the fermentation in a demijohn, with airlock. With UK grapes, you'll have to add a bit of sugar, or bought grape juice.
When the bubble rate dies away, it's done.
As I say, don't hold your breath...