Plants need sufficient aeration and drainage around their root systems, and clay soils are often too compact to provide this. You can amend your clay soil, however, by adding organic material to alter the consistency and nutrient content of the planting bed for your flowers or shrubs.
Till or spade the planting bed to a depth of about 8 inches. If the soil is too hard or in large clods, wet it and try again in a day or two.
Spread the organic material on the soil surface, about 4 inches deep. The more specific recommendation is to add 25-50% "by volume," meaning that whatever volume of soil you're amending should have organic material added which is equal to 25-50% of the volume of the soil. The reason for this target amount is that less than 25% may be to little to provide sufficient aeration, and more than 50% may be detrimental to the plants. If you're unsure about the amount to apply, go with the 4-inch layer rule.
Using your shovel and garden fork, turn the organic material into the soil to a depth of 8 to 12 inches, or as deep as your planting bed allows to accommodate the flowers and shrubs.
Plant your chosen flowers and shrubs according to their specific needs.