Answer: In general, I would suggest you look at a book or two about gardening to try to get a sense of what might need to be done. (There are a number of books in the "Dummies" series that are very good -- practical information that is usable.)
The most important thing you can do is to mow the lawn properly. Set the blade high and mow often enough that you never remove more than one third of its height at a time. This helps keep it dense and thick and enables it to crowd out weeds.
You should also run some basic soil tests to check fertility and pH. The test results will tell you if you need to fertilize or if you need to adjust the pH by spreading lime on the lawn.
With established plantings, you would not need to water unless there is a period of extended dry weather.
Your local county extension should be able to help you with the soil tests and interpreting the results. They may also offer classes and publications on landscape and garden care. In the meantime, their web site may be helpful.
Enjoy your new home and yard!
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