Mike - a balanced fertilizer like the one you mention (30-0-10) will provide a good deal of Nitrogen to feed the turf and some Potassium as well.  Nitrogen is mobile in the soil, being taken up by the grass and washed through the soil (especially sandy soil) so applying it throughout the growing season (when grass is irrigated or growing because of rainfall), you will be providing Nitrogen on a regular basis.  If your lawn is not irrigated and goes dormant, only apply fertilizer in the spring/early summer and/or fall.  See the various schedules you can follow at the bottom of the soil test page.

With both your soil tests showing Potassium at Below Optimum, the easiest way to increase the Potassium is to apply a Potash fertilizer in addition to the balanced fertilizer.  That would boost the Potassium much more than the balanced fertilizer.  Potash is somewhat mobile in the soil but will steadily increase if regular applications are made (again, only when the grass is not dormant).  Too much Potash at one time can burn the grass so it would be best to not apply Potash at the same time as the balanced fertilizer.

For either the balanced fertilizer or Potash product, you can come back to the MSU soil test site and enter the fertilizer nutrient numbers into the Fertilizer Calculator (found under Tools) and the site will calculate how much of each product to apply in one year for 1,000 sq. ft.  Remember to pro-rate the amount if your area is less or more than 1,000 sq. ft.

After a soil test, MSU suggests following the recommendations for 3 years and then re-test to determine the soil health.  Good job starting with a soil test to better understand the health of your soil  Hope that helps!