* Deadhead. To keep flowers blooming, it's important to promptly cut off dead and dying blooms, not just to keep the garden tidy but to prevent the plants from making seed. Setting seed tells a plant that the workday is almost over--that's there's no need to grind out a few more flowers--and the plant can shut down for the season.
This is especially important with some perennials, such as alstroemeria. The whole flower stalk in this case should be sharply yanked from the roots. This will encourage the formation of more flowering stalks. Cut back delphinium stalks so only two or three leaves remain at the stalk's base, and the plants will bloom again in late summer.
On annuals, you simply have to pinch off the fading flowers to encourage more. Of course, this only works up to a point. No matter how diligently you deadhead, flowering will eventually end as the season passes.
* Deep water. Despite the late rains, plants need water several feet deep in the soil, which is the layer where most of the roots are. Plants are growing rapidly now and need a reservoir of water, more than those rains provided. Let sprinklers run long enough to wet this area, but water less often so the soil doesn't stay soggy. Only newly planted items need water every couple of days in spring.