For an annual flower, meaning one that lives only a single season, all you have to do is nip off spent flowers. The reason flowers grow blooms is so they can turn into seeds, and if you nip off the spent flowers before they can do that they'll grow more blooms. They'll continue doing this until cold weather kills them in the fall. It is important to remove the entire bud and bloom, not just the faded petals. Otherwise you leave behind the part that turns into seeds. With many flowers you can easily nip off the spent flowers with your fingers, or you can use a light pruner. Most of the flowers we sell are annuals, for example Petunias, Impatiens, Zinnias and Snapdragons.
Perennial flowers are a different story. They come back year after year, but normally have a short blooming period. You cannot usually extend the blooming period of perennial flowers, but there are exceptions. Usually the exceptions are flowers that are borderline perennial, like Fuchsias. Fuchsias can be wintered over if you protect them from harsh weather, and you can keep them blooming all summer long the same way you would an annual flower.