Summarize:

Using a hose, rinse off the entire soft top hood with water. Make sure to soak the fabric thoroughly, that way you loosen up the material and remove as much dirt, grime, and gunk as possible. If you'd like, you can use a power washer instead of a hose. Just make sure to hold the nozzle at least 2ft (24in) away from the soft top to avoid damaging it. Spray the soft top thoroughly with either auto shampoo, like Chemical Guys Foaming Soap, or a vehicle fabric cleaner, like Ammo Shag Fabric Cleaner. Then, rub the solution with an interior cleaning brush to agitate it. When you're finished, rinse off the shampoo with clean water. For the best results, move your brush in straight line motions. To get dirt out of a corner or seam, tap the area with the end of your brush. For most jeeps, a thorough cleaning should take around 20 minutes. You can purchase auto shampoo and vehicle fabric cleaner at auto supply stores. Over time, stubborn patches of soil, bird droppings, or green mold may stain your jeep's soft top fabric. To remove these patches, shampoo the affected areas and gently scrub them with a stiff bristle brush. This will force the stains up, creating a paste-like substance that you can rinse off with water. As with your interior cleaning brush, move the stiff bristle brush in straight line motions for the best results. Use this technique sparingly to avoid damaging the material. To dry the fabric, purchase a shammy cloth like The Absorber or Mighty Cleaner. Then, press the towel down into your soft top fabric to dry it off. When you've removed as much water as you can, park your jeep in a warm place so it can finish drying. To prevent mold, only air dry your jeep after you've removed as much water as possible. If you'd prefer, you can use a microfiber towel instead. However, make sure you use and wash the cloth a few times beforehand, otherwise it may leave unwanted particles on the hood. Do not use a terry towel or paper towels to dry your hood. Doing so will leave small amounts of residue that are difficult to remove.
Rinse the hood with water. Clean the fabric with auto shampoo. Scrub the fabric with a stiff brush to remove deep stains. Dry the fabric with a shammy towel.