Remove pet hair with a lint roller before steam cleaning. Fur and similar fibers will release from the fabric easily while dry. However, even with a strong, commercial grade steam extractor, you will find that removing hair is a difficult chore once the fabric is wet.
Set-up your steam extractor with the upholstery tool engaged. Mix your cleaning solution according to the manufacturer's instructions. Test the solution in a hidden area of the couch. Even though microfiber furniture should not pose a problem with a steam extractor, it is prudent to still test for colorfastness and compatibility. If color loss or material distortion occurs, stop cleaning and call a professional upholstery cleaner.
Clean the back, sides and cushions of the couch with the upholstery tool. Work with overlapping strokes, releasing cleaning chemical on the back stroke. Use several dry passes to remove as much moisture as possible from the fabric. For heavily soiled sections, such as the armrest and headrest, slide the upholstery tool slowly to allow the chemical more time to work. If necessary, use an upholstery-spotting chemical compatible with your steam extractor.
Set the nap of the couch with a lint free towel. With the towel folded, gently brush the nap down to remove the stroke marks from the upholstery tool. If the couch dries with the upholstery marks, simply re-clean, then use the towel while the fabric is wet to smooth out the nap.