ivy on trees
We do not recommend that you let the ivy grown on the tree as it can deny photosynthsis to the foliage on the branches and cause decline.
First, if it is in trees, cut it off at the base of the tree and paint the newly cut end of the vine with a systemic herbicide (one with the ingredient glyphosate or triclopyr) at a high strength. Do not let the herbicide get on the tree. Also, to make it easier to see what has been removed, cut the vine off again at about shoulder height so that you can easily see a bare area about the tree base. Do not let new tendrils start going up the tree again. Keep it off.
It is okay to keep the ivy growing around the base of the tree if you want. Do not let it get out of bounds.
If you want to tackle the vines on the ground, In the spring, you can pull, prune out or even mow all the vines down to the soil surface, so there are no mature leaves left and you've removed as much vine as you can. This will not kill the vine because its roots store lots of energy with which to grow new leaves. However, the roots will have to use up that energy to start new leaves. (You can also physically pull or dig up root, of course.)
We are not sure how much you are able to control. See the attached link on English ivy for more information. http://www.nps.gov/plants/alien/fact/eufo1.htmmh