Look for suckers or daughters growing from the roots of the raspberry plant. They will be growing separate from the mother plant.
With a spade or shovel, carefully dig around the sucker. Keep as much soil around the roots as possible. Use a scissor or pruning shears to cut the main root that attached it to the mother plant.
Find a pot large enough to hold the sucker you've just dug up. Make sure it has drainage holes for water to seep out.
Add potting soil in the pot. Place your raspberry plant inside and finish filling the pot with soil. Water the sucker or daughter thoroughly.
Put the sucker transplant in a sheltered area of your garden. This will give your transplant a better start on developing more roots. In a month or so, when the roots have developed more, prepare the garden soil.
Dig up the soil with a spading fork or tiller. Add 2 to 3 inches of compost and work this into the soil.
With a shovel or trowel, dig holes that are bigger around than the raspberry's container. Make the holes about 24 inches apart, spacing each row 7 to 8 feet apart.
Pop the raspberry plant from the container, and place it in the hole. Make sure the soil ball does not protrude higher than ground level.
Fill the hole with soil. Firm the soil so there are no air pockets. Water thoroughly. Keep the soil moist but not soggy until the plants are established.