Soil Preparation
Leeks require a rich well drained area of soil. You can dig in plenty of well rotted compost with plenty of moisture content.
They can be placed in full sun or partial shade, but hate to be water logged.
Note: I found when I had my leeks in a gloomy dark corner of the allotment they bolted to seed and were inedible.
Sowing Seeds
You can start seeds either in trays or directly in the ground (once the danger of frost has passed).
Sow seeds about half an inch deep, with an inch between seeds. Seedlings should emerge in about 2 weeks if you planted directly in the ground, maybe sooner if you sowed them in trays and kept them warm/indoors.
Thin seedlings out to roughly 4 inch apart.
Transplanting
When leeks are about 6 inches tall, make holes 4 or 5 inches deep and about 8 inches apart, you can use a fancy garden tool or your fingers. Place one leek seedling into each hole.
Do not fill the hole with soil, instead fill the hole with water. This will give the roots space to spread out and will backfill the hole a little for you, gradually filling completely over the course of a few weeks.
Plant Care
Leeks are very hardy plants, once in the ground you could leave them alone and they would very likely survive and continue to grow for many months before going to seed.
You can however blanch your leeks.
Increase the white portion of each leek by carefully earthing up soil around the bottom of the stem gradually over summer.
Some people use old toilet rolls or brown packing paper, this both blanches the stem and stops gritty soil getting into inside the leeks.
Harvesting
You can harvest the leeks when young or leave them to mature. Simple use a fork to gently lift leeks leaving the rest to carry on growing.