Prepare the barrel by drilling a dozen or so drainage holes in the bottom of it. Place the barrel in its permanent location in your garden -- once it is full of gravel and soil, it will be difficult to move. Raspberries need at least six hours of full sunlight every day, so keep this in mind when placing the barrel.
Fill the bottom of the barrel with 3 to 4 inches of gravel. Fill the barrel the rest of the way with a mixture of one part organic material like compost or well-rotted manure, one part sand and two to three parts soil. You may purchase potting soil or use soil from your garden.
Add 1/2 to 1 cup of balanced 10-10-10 type fertilizer to the soil and mix it well. Push the soil aside to make two or three holes that are about as large as the young raspberry plants' nursery containers. Lift the plants out of the containers and place them in the holes. Hold them up and pack the soil in around the roots.
Water the young raspberry plants thoroughly until the soil is quite moist but not soggy. Use a garden hose with a misting nozzle to water often enough to keep the soil from drying out. Raspberries are fairly drought resistant, but don't let the soil stay too dry for too long. Water every three days or so.
Prune your raspberry plants shortly after harvesting the berries. Once the fruit has been harvested, the canes start to wither and die. Cut them down at the end of the growing season and they will be replaced by new growth the following spring.