Answer: First off, I should mention that lawn grass grows best in full sun all day or for a minimum of half the day and does not compete well with tree roots. If these conditions exist in that area of the yard, you may want to consider using a ground cover of some sort instead of lawn grass there.
In general, you would need to remove existing vegetation,remove larger stones and rocks,loosen the soil down about six inches, work in a generous amount of organic matter such as compost (critical step if you have poor soil), add fertilizer and/or lime as indicated by soil testing, level the area and rake it smooth before planting.
Unfortunately, this is the worst time of year to try to start a new lawn because the weather is so hot and there are often dry spells in summer as well. The best time is late summer to early fall. This does allow you time though to run the soil tests and plan your work.
Your local county extension should be able to help you with the testing and interpreting the results, and suggest the best types of grass for your particular soil and growing conditions.
Good luck with your project!
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