Answer: First off I should mention that often English ivy (Hedera helix) was planted as a groundcover. Groundcovers such as this are typically used in areas where lawn grass will not thrive. This can be due to too much shade or to competition from tree roots or to a steep location that is unsafe to mow. Groundcover such as this provides a visually soothing flat green space similar to lawn but with absolutely minimal maintenance work. So sometimes removing the ivy is not really such a good idea as it can result in a bare area that is difficult to replant.
Assuming you think there is a good change lawn grasses will grow there (at least a half day of direct sun with all day being preferable and a reasonably decent soil), be prepared for a large job. Removing the ivy will be difficult and may take a sustained effort. The reason for this is it is deep rooted and has what could be called an iron constitution. Pulling it up is not going to be successful -- besides being time consuming. You would need to grub out the roots as best you can in addition to pulling away the surface vines. Most people opt to use an herbicide containing glyphosate as well. If you use this be sure to carefully read and follow all of the label instructions. It may require more than one application, too. In a smaller area you might be able to smother the remaining ivy by covering it with several layers of damp newspaper or cardboard topped with a thick layer of organic mulch. Eventually it should die due to lack of light. This has the added benefit of beginning to improve the soil in the planting area when it decays over time. To plant grass, you would most likely need to add organic matter to your soil and the rotted down mulch would do this.
Prior to planting grass either by seed or sod you would need to run some basic soil tests and see what amendments (such as lime or specific nutrients) might be needed, and in what quantitites. The soil would be loosened and organic matter such as compost added to prepare a good environment for the grass roots, the area should be fine graded and leveled, and the texture should be tilled and/or raked smooth to provide a seedbed if you seed.
After tilling, you will need to allow several weeks for the weeds to germinate and then kill them off prior to planting. (Tilling brings dormant weed seeds to the surface where they can grow, so the more you can eliminate prior to planting the lawn, the better.) This also allows time for the soil to settle a bit so you can fine tune the leveling prior to planting the lawn.
Fall is a good time to install a new lawn because rainfall is typically generous at that time and the roots can grow until the ground freezes while the temperatures are also cooler and thus less stressful on the grass. YOur local county extension should be able to recommend the best lawn grass types for your particular location and provide lawn installation and maintenance instructions suited to your area. They can also help with soil testing and interpreting the test results. Best of luck with your project!
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