Plants need both major and minor nutrients. Minor nutrients (also called "trace elements") are usually supplied by the soil, but plants use major nutrients in large enough quantities that we should add them regularly.
Of the major nutrients, nitrogen (N) is associated with green, vegetative growth; phosphorus (P) is associated with flowering; and potassium (K) aids root development. However, that's an oversimplification. All three major nutrients are necessary, to some degree, for all aspects of healthy plant growth. If plants don't have enough nitrogen or potassium, they're unlikely to flower well, even though there's plenty of phosphorus in the soil.
"Stop fertilizing most perennials after midsummer."
There is no one best fertilizer formulation for annuals or perennials. Many work well. However, choose a fertilizer that's higher in phosphorus and potassium than nitrogen to encourage blooming and discourage excessive leafy growth. If you're growing perennials primarily for foliage, use a balanced fertilizer with equal parts N-P-K.
Fertilize annuals throughout the growing season, and perennials from spring through midsummer. Stop fertilizing most perennials after midsummer so they'll slow their growth and prepare for winter dormancy. Perennials that are still putting on new growth in fall will be vulnerable to winter injury.
Some newer annuals do better with frequent fertilizing (every 10 to 14 days), particularly if they're growing in containers. An easy way to provide enough nutrients is to mix slow-release fertilizer pellets into the soil when you plant. The pellets will release nutrients into the soil for about three to six months.
Deb Brown is professor emeritus at the University of Minnesota Department of Horticultural Science.