This video of a quick an easy microfiber sofa cleaning is simple and effective. I'm a professional upholstery cleaner in Tampa FL and I can tell you that this is an easy way to clean a microfiber sofa. The solution being used will emulsify soils and loosen oils in the polyester based microfiber.
There are a couple of things I would recommend to help with the cleaning procedure. First, use carbonated water instead of distilled. Second, use only 7 drops of dish detergent to every cup of carbonated water. It will be just as effective without leaving soap residues on the surface after cleaning. I would also replace the brush with a softer horse hair brush so the microfiber does not get weakened. The last thing I would mention is after brushing the surface with the cleaning solution you should light spray of plain water over the sofa before towel drying.
These changes are not big changes to the process and it will give you a better microfiber sofa cleaning then what the video shows. However, if you just follow the steps in the video it should clean alright.