What home remedy can I make to keep the deer away from my vegetables?

Try sprinkling soap shavings around your garden- once they get a mouthful, they won't come back. Just make sure to replenish after a rainfall.

go to your local barber or stylist and ask them to save their hair clippings for you.

Sprinkle the hair around the garden and you are golden.

Big dogs works every time...

All the above are good techniques, use them all. The best way is to use multiple techniques and rotate them. The spray I use regularly, though, is a homemade spray of hot peppers, cayenne pepper, and anything else hot. Mix in a blender with water, strain with cheesecloth and spray! Spray weekly and after it rains.

Blend up a raw egg and 2 cups of water and spray your plants. You can also add hot pepper if you wish. Deer stay away from egg smell, but you need to reapply frequently.

I was told that human hair is a deterrt

sorry, about the above, but it wouldn't let me backspace to correct my spelling. Anyway, get human hair from your local beauty shops. That is supposed to be really offensive to deer. A fence might work too, but is more expensive than hair.