Turn your chair/settee upside down and remove staples from the platform cloth around the area where you suspect the broken spring is. If necessary remove castors by gently levering with an old screwdriver.
Once enough of the platform cloth is unstapled, fold it back and inspect the springs. If they are fitted individually and one spring is broken use a lightweight pin hammer and tap the end of the spring sideways through the retaining clip taking care not to dislodge the clip. See attached sheet on retaining clips for more information.
Measure both parts of the existing spring and order replacement.
Fit replacement spring into existing clips by gently tapping the kinked end of the spring through the opening of the clip. (Take care not to disturb the plastic insulation in the clip because this is what prevents the spring from squeaking when in use).
The spring should arc upwards so that the sitter will depress it.
To finish the job check that the new spring is not loose in its clips and if is then tie it to springs on either side so that there is no chance of it slipping out later.
Replace the platform cloth and casters.
RETAINING CLIPS FIXED TO SPRING RAIL
These clips are fitted before the frame is upholstered. Because of this it is difficult to replace them if they become dislodged during replacement of the spring. Most clips are stapled or nailed to the top of the spring rail but some clips are held in place by a metal prong which is a part of the clip and digs into the back of the spring rail.
To replace a dislodged spring clip where you are unable to nail down from the top of the frame it is possible to drill a pilot hole into the inside edge of the frame and using a self tapping screw and a washer fix the clip here instead.