Partner selection
In my opinion it is best to start with a group of semi-adult fish and let a couple select themselves, don't believe the couples for sale in a lot of petshops. Often they are just two mature fish and a discus couple is really something different, discus are very picky when it comes to their partner choice. That's quite normal in the animal world when a couple have to depend on one an other in raising their young, and discus are no exception. When a couple is formed within a group of discus fish the change of getting a successful breeding couple is much better.

Water conditions
For discus breeding the water hardness and PH value are very important, be sure to keep the values as close as possible to the optimum, otherwise the discus will spawn but the eggs will not develop correctly.

The optimum water conditions for breeding are:
Temperature: 31°C ( 88°F )
Hardness: 3-10° dGH
Ph: 5.5-6

A breeding tank?
If you need a special breeding tank depends on a lot of factors. Are the discus kept by themselves or do they have other species as tankmates. You can imagine that if other species of fish are present they can disturb the couple and/or feed on the young. The discus will try to protect their young but in the limited space of an aquarium that is hard to achieve. If there are only discus fish present and the tank is not overcrowded you have a good change a couple can raise the young within the tank.

If you want to raise as much of the young as possible and want more control on the water values and other variables, a special breeding tank is the preferable. This way the couple can solely concentrate on their care of the young and it makes the feeding and cleaning for the hobbyist much easier. I personally like the more 'natural' breeding method within the regular discus tank. You will probably loose some of the young, but the behavior of a breeding couple within the group is worth it.

The eggs
The discus couple will find a suitable place ( plants, aquarium window or any other vertical place ) to deposit their clutch of eggs, the amount of eggs ( 50 to 200 ) depends on the size of the female discus. They start cleaning the place very carefully and often the surroundings as well, this is part of their mating behavior. While cleaning the place, they shake their heads and often are aggressive to curious tankmates. When al the cleaning and shaking and stuff is done the female will start laying her first row of eggs, the male discus follows behind her to fertilize the eggs. The eggs will hatch in about 60 hours.

To raise the young discus you need to start you own little Artemia factory, more information about artemia as a food source here.