Answer: The most important thing you can do for a lawn is to mow it correctly. Mow it high at three inches, and mow often enough that you never remove more than one third the grass height at a time. In the spring, this can mean mowing more often than once a week.
The other overall very helpful thing to do is run some basic soil tests to check the soil pH and fertility levels. Then fertilize and/or add limestone to adjust the pH as indicated by the test results. This helps keep the grass growing vigorously so it can crowd out weeds.
If the lawn seems thin and you need to overseed or reseed, September is the best time of year for doing that. The following information should help you trouble shoot and develop an overall maintenance plan for your lawn. You may need to cut and paste the complete url into your browser to make it work correctly.
Your local Cornell cooperative extension should be able to help you with the soil testing and interpreting the results and working out a maintenance plan based on the existing lawn conditions in your yard. Enjoy your new home!
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