The purpose of fertilizing is to add nutrients that grass needs so it can grow, develop a healthy and thick root system, have plenty of resources to draw on during the hot days of summer and the cold days of winter, and have healthy and thick growing pattern to discourage weeds.
Doing a soil test before you apply any sort of fertilizer is a great idea, and will help you apply the right kind of fertilizer in the right amounts so that your grass actually benefits.
Plan on 3 - 5 applications of fertilizer per year for most types of grasses, but be aware that the amount of fertilizer will vary depending on what type of grass you grow (if it is a vigorous grower, such as Kentucky bluegrass, you may need an additional application) and whether you mulch or bag your grass clippings. Mulched clippings, which return to the lawn and disintegrate, leave their nutrients back in the soil so yards may not need as much fertilizer.
Fertilize when the lawn is growing, which will differ for warm-season and cool-season grasses. Warm-season grasses usually need several small "fertilizer meals" over the summer, while cool-season grasses will benefit most from a couple of heavier "fertilizer meals" applied in the fall.
Slow-release formulas are safest and usually best for grass. If you use a liquid fertilizer with a quick-release nitrogen, you'll need to reapply more often. If you do want a quick surge of growth, as opposed to slower, steadier growth.
Plan to fertilize right before a rainfall, or water your yard thoroughly after fertilizing. This practice will wash the fertilizer off the leaves of the grass and down into the soil, where the root system is.
Using a spreader will help you maintain an even spread over your whole yard.\
Sources:
Scotts Lawns: Your Guide to a Beautiful Yard by Nick Christians with Ashton Ritchie
