Here's a tip I discovered while restoring these burnt orange chairs. I was going to rent a steam cleaner to clean them up, but did some google searching and found that some recommended using a wet-dry vac (ie. Shop-Vac) to do the same job. So I mixed some hot warm water with a little bit of laundry soap (I used the mild hypo-allergenic type) in a large spray bottle, sprayed it on, and vacuumed it up right away. It seems like that's all that a steam cleaner does anyway. After that and a bit of vinyl cleaner, I thought they turned out really nice. I've since refined the technique a bit, and I now use two spray bottles: one with dilute laundry soap and another with plain warm water. After cleaning with the soapy water, I'll do another cleaning with just the warm water to get more of the soap out. I use an auto upholstery attachment (like one you would find at a coin operated car wash) on the wet-dry vac. Here's a before and after picture.
If you already have a wet-dry vac (the more powerful, the better), this might save you a steam cleaner rental fee. Plus, I like that it doesn't require that you use harsh chemical cleaners. I would also recommend that you try to get out as much dirt as possible by dry vacuuming first. It seems like the more dirt you can get out before wetting it, the better.