Here are some evidences of grapes grown outside our house garden in Sg.Buloh, Malaysia.
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All you need to do is plant the grape seeds after eating the fruit. Make sure there is plenty of room for the plant to creep e.g. on a pergola. Not sure if it can grow nicely on fence.
However, the size is smaller than those seen in hypermarkets and it needs some time (approx. 12 months) and luck to fruit. The plant in the pictures was planted 18 months ago.
If you are thinking of plating grapes now, make sure you have lotsa patience!