Start with a soil test. Based upon the results adjust the pH first and
then provide nutrients as required.
Most extension centers can provide a soil test or direct you to a soil
test for a nominal fee.
Mow often enough to return the grass clippings to the lawn where they
can provide food and organic material to improve the soil.
Half of the lawn's nitrogen input can be provided by just returning
the clippings to the soil either directly or composted and applied as
top dressing.