The time for sowing depends upon where you live. What to plant depends upon the season and weather.
Vegetables are generally divided into two categories: cool-season crops and warm-season crops.
Cool-season crops and warm-season crops:
Cool-season crops should be planted so that they mature when the weather is cool, either in spring or early summer or in autumn or winter. Cool-season crops come to harvest in cool weather, either in spring or fall or winter. Cool-season crops can be planted when the soil and air temperatures are cool, as low as 40ºF (5ºC). Mature cool-season crops can survive in temperatures near freezing without protection. Cool-season crops do not do well in the warmest summer temperatures.
Warm-season crops should be planted so that they mature when the weather is warm, when the soil and air temperatures are above 50ºF (10ºC). They will grow best when the temperature is 75ºF (24ºC) or warmer. Warm-season vegetables can be grown out of their season if they are protected from temperatures below 50ºF (10ºC).
Hardy and half-hardy crops:
Cool-season vegetables are often further categorized as hardy and half hardy.
Hardy vegetables are the most cold tolerant. They can be planted 2 to 4 weeks before the date of the average last frost in spring; their seeds will germinate in cold soil and their seedlings can endure short freezes. Hardy vegetables will grow when the daytime temperature is as low as 40º (5ºC) degrees. Hardy vegetables include: asparagus, broccoli, Brussels sprouts, cabbage, chives, collards, corn salad, garlic, horseradish, kale, kohlrabi, leeks, mustard, onions, parsley, peas, radishes, rhubarb, rutabaga, spinach, and turnips.
Half-hardy or semi-hardy vegetables grow when the minimum temperature is between 40º and 50º (5-10ºC). They are able to tolerate light freezes, that is just a few hours of frost. Half-hardy vegetables include: beets, carrots, cauliflower, celery, celeriac, chard, Chinese cabbage, chicory, globe artichokes, endive, lettuce, parsnips, potatoes, salsify, sorrel, and hardy herbs. Half-hardy crops may be planted as early as 2 weeks before the average last spring frost.
Cool-season vegetables grow best when the temperature highs are in the range of 70-75ºF (21-24ºC). Cool-season crops usually stop producing when daytime temperatures reach 80ºF (26ºC) or higher. Many cool-season crops that come to maturity before or shortly after the first frost in autumn can be protected where they are in the garden from freezing temperatures and harvested as needed throughout the winter. (These plants do not continue to grow, but simply maintain and remain ready for harvest.)
Tender and very-tender crops:
Warm-season crops are often categorized as tender and very-tender.
Tender vegetables prefer temperatures between 70º and 95ºF (21-35ºC) and require daytime temperatures of 60ºF (15ºC) or greater to thrive. Tender vegetables will not tolerate frost and may be sensitive to cool winds. These crops should not be sown in the garden until the date of the average last spring frost. Tender crop seedlings are best transplanted into the garden 1 to 2 weeks after the last spring frost. Tender vegetables include: beans, celery, sweet corn, cucumbers, New Zealand spinach, summer squash, and tomatoes.
Very-tender vegetables require daytime temperatures consistently warmer than 55ºF (13ºC). A week of daytime temperatures below 55ºF will likely stunt the growth of a very tender vegetable. These crops are likely to suffer in a cool breeze. They are best planted at least 3 weeks after the last frost in spring. Very-tender vegetables include lima beans, cantaloupe, eggplant, muskmelon, okra, peppers, pumpkins, winter squash, sweet potatoes, and watermelon.
Protecting out-of-season crops:
Many warm-season vegetables can be grown out of their season if they are protected from temperatures below 50ºF (10ºC). Vegetables can be protected from low temperatures with cloches, row covers, cold frames, hot bed, and greenhouses.
Tender plants started under protection should not be set out before the date of the first frost. Plants started in a cold frame or under cover should be hardened gradually by exposure to the outdoor air before transplanting.
Seeds and transplants should be planted in workable soil, which means not too cold or too wet. Planting in cloudy weather or at evening or early morning will safeguard against wilting.
A starter solution of compost tea (a handful of compost soaked in a gallon of water) is all the first watering seeds or transplants need.
More tips at Vegetables in the Right Season.