Mark the edge of your planting area around the tree. This should be well beyond the spread of the branches (the dripline) so you don't damage the tree's roots. Ensure the shape of the planting bed goes with the rest of your yard. If you have formal landscaping elsewhere, choose a circle or square planting bed. If your landscaping style is more relaxed, mark out an irregular area that coordinates.
Add mulch in the fall instead of digging out the lawn. It will break down and add a layer of soil in which you can plant next year. The heavier the leaves are that drop from the tree, the more mulch you can add. Don't go up the tree trunk, as this can sometimes lead to rot. Gradually increase the thickness of the mulch as you move away from the tree.
Plant the plants and flowers in the spring. Choose ones that naturally grow under trees in a forest, such as ferns, astilbe, columbines, hostas and bleeding hearts, or groundcover such as mint or sweet woodruff. Selecting compatible plants will increase their chances of survival. Arrange the plants so the taller ones are closest to the tree and the shorter ones are beyond the branches. Next to the lawn, you may be able to plant flowers that require more sun and nutrients.