A: You can dig up ivy fall or early spring and move it. If you are in a really cold climate you will best results transplanting in the spring.
Dig around the base of the ivy stem leaving as much root & soil as possible. Dig the new hole wider and deeper than the root ball. It is good to plant ivy deeper-- as much as 3-4" deeper if possible. That will secure the ivy in the ground and help to prevent drying while it acclimates to the new location. Water regularly making sure the ivy does not dry out but do not keep the soil too wet.
I would suggest mulching with almost any organic mulch like pine needles, leaves or chipped bark. This also helps to keep the soil moist and the temperature even.
You will need to give the ivy some TLC for the first few months but once it gets started it should be fine. It is always a good idea to keep newly planted ivy carefully water for the first year or so. After that you can practically ignore it (depending on your climate) and it will survive with the natural rains or normal garden irrigation.