Leeks are a cheap food to grow from seed, you get hundreds of seeds in a pack.
They can be sown straight in to the soil, but leeks sown this way have a lot of leaf and not much stem, which is the bit we want the most of! So to get a long white parthey have to be transplanted and buried deeper in to the soil. Therefore most gardeners start them off in a pot or seed tray in spring and then plant them out into their final place in the summer.
This video from Allotment Diary gives a really good way of using a deeper box to get really strong fat seedlings to plant out. These will make for a bumper crop.
You can also sow seeds into modules, you can do one plant per small module or several in a large module. This video from Work With Nature shows you how to plant seeds in modules. It also shows you how to save your own seed from a leek seed head. Leeks are biennial so if you want to save your own seed you need to leave a leek plant or two in the soil to the second year when it will grow a seed head to harvest. The heads are very pretty. Some people plant them in their flower beds as the heads are tall and striking.