I had an off-white upholstered rocker that I suddenly realized was filthy. Funny how that kind of thing can sneak up on you.... Anyhow, I worked on it first with a can of upholstery cleaner. It was somewhat better, but then I realized that the bottom of the skirt was black with dirt. The foam cleaner didn't touch it. Then I tried my Shark hand-held steamer. I blasted a small section of the skirt fold with steam, then rubbed it with a microfiber cloth. A Lot of dirt came off. After working my way all around the edge I tackled the rest of the chair. It helped, but didn't get all the dirt off.

Long story short, I tried to donate the chair to Goodwill but they wouldn't take it. I ended up driving it to the dump.

Assuming your furniture isn't as dirty as my chair was, I recommend trying steam. It really loosened a lot of the dirt. Just don't wait as long as I did.