Spring is the best time to plant flowers for the summer. You are past the harsh cold of winter, and the ground is thawing. A good month to start planting is April. Typically frosts are done for the season, and the rains are starting, which softens up the earth. Planting at this time gives your flowers a good chance of survival.
Till up the garden where you can with a hoe or small tiller. The soil has been sitting for a while without much work being done, and this will bring in much needed oxygen. Mix in whatever mulch is left over from the prior year. It will break down more in the dirt and make it even richer.
Mix in fertilizers or compost to feed the soil and give the new plants something to eat.
Check on perennials and water them.
Dig holes with a hand trowel or shovel for the various flowers you want to add. It is best to put in plants that haven't already started blooming. They are less likely to be root-bound or go into shock from the transplant.
Set flowers in the holes, making sure the root balls will fit.
Fill in the holes with the surrounding soil.
Spread new mulch around all the plant beds and then water until damp. The mulch will trap the moisture and keep the flowers hydrated.