Shambani Organics, Shingletown, California

Transplanting is hard on any plant, but if you use the following tips, your plants will suffer less shock:

"Harden off" your seedlings by exposing them gradually to full sunlight and cooler nighttime temperatures. Keeping them moist, give them one hour of full sun, then two hours, then a morning or two and finally a full day. Follow this same pattern for the cool of night, all before you put them in the ground outside.
Transplant on a cool, cloudy day or just before sunset, and provide shade from the full afternoon sun of the day after transplanting.
When separating multiple seedlings do your best not to disturb the roots. Also when removing a seedling from its container, wait until the last possible moment to prevent the roots from drying out.

Water the hole you've prepared for the seedling, cover its roots, and water again. Don't pack down the soil too firmly; let the water do it.
Relative soil surface level is unimportant for many plants; however some must not be planted to deeply. Bury only the roots of squashes, cucumbers, melons, and others; the "crown" where the stem begins should be on the soil level. Conversely, tomatoes can be planted quite deeply; roots will develop along buried stem.
Gently handle seedlings during transplanting by their leaves, not stems.
More tips can be found in the plant varieties section of this site.