Confer with your state conservation or natural resources department for lists of plants native to your area. The Missouri Conservation Department for example, in conjunction with the Missouri Department of Agriculture, maintains an impressive database and resources for the promotion of native plants in the landscape called GrowNative! (Grownative.org). Other states maintain similar databases.
Determine the location you wish to plant and study the characteristics of the space for ideas of sun/shade, moisture, soil type and other applicable conditions your plants will encounter. Choose which plants will work in that situation by comparing to native plant lists with similar requirements.
Decide the intended use for this area---play, pasture or meadow, or aesthetic enjoyment---to further determine which plants are appropriate in your specific location. Some plants will be more fragile than others, so match plants to use carefully for maximum benefit.
Prepare the area for planting by removing all turf and weeds that may compete with emerging seedlings. According to Stock Seed Farms, "Planning a year ahead allows the best chance for success. Eliminating sod forming grasses... may take more than one application for complete control."
Direct sow by hand in smaller areas; use a mechanized seed drill to sow large areas like fields. Small plantings, especially flowerbeds, may be planted directly with potted plants from native plant nurseries. Sow grasses and flowers separately since flower seeds may not emerge if planted too deeply (as is recommended for native grasses).
Firm the seedbed with a weighted roller or by walking over it, to ensure good soil contact around seeds. Keep planted areas moist and weed free until seedlings are established. Be patient--perennials need many years in which to send down deep roots before reaching their peak for flowering.