Having just chopped down a monster privet, my first though would be 'why would you want to grow a privet hedge?' But if you absolutely must then just take semi-ripe cuttings, about 12-15 inches long, strip off the lower leaves and stick them in a pot of compost.
But there must be loads of shrubs that make much nicer hedges.

Hi, welcome to G O Y, I agree with Urbanite, I have a privet hedge at the front, and about halfway down the side of my garden, and believe me, they are a right royal pain in the proverbial, for your own benefit, grow something else, Derek.

I agree too - they are very greedy feeders and will take all the goodness out of the soil.

Really? Would Boxus have the same effect?

I don't think so but it grows a lot more slowly. What height hedge are you after and in what position? There will probably be other options.