Answer: First evaluate the area to see if lawn is feasible. Lawn needs full sun all day or at least half the day, and reasonably good soil and steady soil moisture to thrive. It also requires constant maintenance and regular mowing at some expense. For mowing safety, the lawn area should be relatively flat as well.
Very often ivy was planted as a low maintenance groundcover in an area where lawn grass just will not thrive. For example, in shade, poor soil conditions, steep slope, surface tree roots all prevent a healthy lawn. If you are certain you want to grow lawn, you can remove the ivy by using an herbicide containing glyphosate. Read and carefully follow all of the label directions. You will likely have to repeat the process one or more times. You can also dig it out by the roots, but this process will usually require follow up digging and possibly herbicide treatments as well.
Ivy has very deep roots and is a "survivor" plant so it can be quite difficult to eradicate. If you simply want to control its spread, you can pull up the new growing tips or runners on a regular basis and trim it back as needed.
It is not a good idea to allow ivy to climb trees, so you may want to cut the stems of the ivy at ground level. Ripping it down may not be possible, but eventually the foliage will drop and the vine will deteriorate over time.
Ivy can actually protect a wooden fence from the elements and gives it a natural look so it seems to fade into the landscape. If you want to remove the ivy from your fence, keep in mind that its holdfasts or little hairy roots will remain on the fence after you rip down the vine. This is not very attractive. Again, something to consider before you remove it.
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