The ideal planting-out day is cloudy and damp with no wind. In our area that is rare, so second choice would be late afternoon after the heat of the day has passed. Loosen the soil in a larger area than you will need for the pot, then dig a hole. Put some compost or a little fertilizer in the bottom of it before turning the pot upside down, tapping on the bottom and easing the plant out. If the roots are root-bound, gently try to tease them apart a little with your fingers. As you set each plant in its hole in the ground, water it in and then cover the roots with fine loose soil. On a bright, sunny day, you should cover the seedlings with berry baskets or a span of fabric row cover for shade.
Keep a close eye on them in the following days to detect any problems before they develop. When plants are transplanted, growth will usually be set back by 1 - 2 weeks as the roots establish themselves, after which they will quickly catch up.
So what can go wrong? Some experts say the most common problem is starting seedlings too early. This can result in rootbound plants and leggy weak growth.
Not hardening off plants adequately can cause several weeks of setback and, in the case of cucumbers and cauliflowers, result in little or no crop.
Take care when planting out peat pots, and tear away the top rim of the pot. If even a small piece of peat pot is exposed after transplanting, it will draw water from the soil surrounding the transplant's roots, leaving the plant in danger of water stress. Also, many gardeners slit the side of the pots to ensure the roots can penetrate the sides.
Tomatoes can grow roots from the hairs on their stems, so if your plant is excessively leggy, you can plant it deeper than it was in the pot. Dig a trench and lay the tomato plant in it horizontally, just leaving a few leaves above the soil line. Fill in the soil and and water well. After a few days, the plant will grow upright.
Why not sow seedlings in large pots to start with? It's more expensive in compost/soil mix and takes up more room; more importantly, it doesn't encourage the seedling to produce a compact root ball, which in turn encourages more compact growth, rather than leggy spurts.