It very much depends on the size.
If it consists of a row single conifers that are, say under 4 ft, it is usually best to loosen the soil on each side and then swing on the top so that the roots loosen & come out.
However for any hedge bigger or more complicated than this, you will need to saw off as much top growth as you can and then dig out the roots. It's a very long and arduous job and then you have to get rid of all the branches. So probably worth getting a quote from someone with the the right equipment to do it by brute force. Don't forget to check that they are including disposing of the rubbish in the price. Try Trees in your Yellow Pages.