Use the nozzle on the vacuum cleaner to suction off any loose cobwebs or large clumps.
Roll a lint roller evenly over the fabric, to pick up the stray sticky pieces. Use a fresh piece on the lint roller, if it is no longer picking up the cobwebs.
Machine wash the fabric, if it's washable, using the setting recommended for the type of material.
Use a cobweb cleaning solution to treat material that still retains traces, even after using the lint roller. A cobweb remover specifically breaks down the adhesion properties of the web, making it easier to remove.