You will need to be careful when you clean a tassel on a lampshade as they are delicate and can easily unravel.
Spread the tassel apart on a small rubber mat or piece of plastic like a plastic bag. Use a dry toothbrush to gently brush the tassel downward and manually remove all the dirt, cobwebs, and grime from the tassel.
If the tassels are still dirty, you can make a cleaning solution by filling a spray bottle with room temperature sparkling water. Add 1 tablespoon of mild detergent.
Then spray a drop of the cleaning solution at the top of the tassel. Carefully brush the cleaning solution downward on the tassel to clean it. Dry the tassel with a clean towel by gently dabbing it.
Work on one tassel at a time until all the tassels are clean.