Ohio is in USDA Zones 5 and 6, which means the expected last frost dates are approximately April 27 to May 31 and the expected first frost dates are approximately September 19 to October 14. Planting a garden in Ohio requires planting frost-tender plants after last frost and paying attention to other weather cues for more frost-hardy plants.
Frost-tender plants are plants that will die if exposed to freezing temperatures. Many annual flowers fall into this category, such as begonias, coleus, forget-me-knots, impatiens, marigolds, morning glories, nasturtiums, petunias, strawflowers, sunflowers and zinnias. Many of these flowers may be started indoors under a sunlamp or in a sunny window and planted outside as seedlings after frost. If a late frost does come after they're in the ground, these plants must be protected, using a plastic or fabric cover until the frost has dissipated. Vines such as morning glories are best direct-seeded outdoors after the last frost.
Several vegetables are also frost-tender, such as celery, corn, cucumbers, eggplants, melons, peppers, snap beans, tomatoes, winter squash and zucchini. Tropical vegetables, such as cucumbers, tomatoes, peppers and eggplants, will do even better if planted a few weeks after the expected last frost, when temperatures are reliably in the 50s at night and at least the 70s during the day. As with frost-tender flowers, these plants must be protected from frost or they will die. Corn, cucumbers, melons, squash, and beans grow quickly enough that they can be direct-seeded outdoors, but other vegetables grow slowly enough planting seedlings will yield much more produce before fall frosts.
Most herbs are not frost-tender, but basil, dill, and cilantro (coriander) are popular exceptions. These may be started indoors, purchased as seedlings or planted as seeds.
In most cases, frost-hardy flowers will be perennials, meaning that they live multiple years. When selecting these plants, pay attention to the hardiness zones listed on their tags. Since Ohio is in zones 5 and 6, anything with zone 5 or less should tolerate Ohio winters and grow again the next spring--though they may need protection in a particularly cold winter. Examples of perennials that survive in Ohio are asters, astilbe, bleeding hearts, carnations, coneflowers, daylilies, foxgloves, hollyhocks, hydrangeas, poppies, shasta daisies and all kinds of bulbs, such as crocuses, daffodils, glory-of-snow, irises and tulips.
Frost-hardy vegetables are almost all annuals. (The few exceptions include asparagus, artichokes, and rhubarb.) These vegetables may be planted as soon as the ground can be worked in the spring, which will be several weeks before the last frost. Direct-seed beets, carrots, fava beans, lettuce, kale, parsnips, peas, potatoes, spinach and turnips outdoors. Several of these may be planted the previous fall (if your garden beds are prepared in time) for quickest emergence in the spring; garlic in particular benefits from fall planting. Broccoli, Brussel sprouts and cauliflower should be planted as seedlings in order to ripen before the heat causes them to bolt (grow past edible stage). Plants in the allium family, such as onions and leeks, should also be planted as seedlings in order to assure adequate growth during the season.
Many herbs are frost-hardy perennials. Chives, fennel, feverfew, hyssop, lavender, mint, oregano, thyme and wormwood may all be planted one year (after the last frost is usually best for the first year) and will come back in subsequent years. Parsley is a biennial, but may be planted as soon as the ground can be worked--though it requires plenty of water and patience before it germinates.