Cut the jonquil foliage after it browns in the fall with a pair of pruning shears. Leave about 3 inches so you can still see where the clumps of jonquils are growing.
Remove a jonquil clump from the ground, using a pitchfork. Dig around the edge of the clump and cut down and under, being cautious not to harm the bulbs. The tops of the jonquil bulbs are typically 5 to 6 inches beneath the soil. In light sandy soils, they may be 8 inches deep. Dig down a couple inches farther to get under the entire clump of bulbs.
Brush off the soil and pull apart the bulbs that are attached to one another. Small offsets may be up near the crown of the plant; pull these as well. Continue to separate the bulbs. Discard the ones that are rotted or damaged.
Replant the jonquil bulbs as soon as possible, 1½ times deeper than they are wide, and about 6 to 12 inches apart. Smaller jonquil bulbs may not bloom for a few years; plant them in another part of your garden, such as the back, to transplant later.