Many great suggestions above.
You can get started with a horsehair brush and some towels. This used to be called shampoo method but using today's encap products its encapsulation or using the towels its like padcapping. Apply the product of choice with a small hand sprayer and scrub. You can also just dip the brush in a bucket and apply that way if you want. Follow up with a towel which will remove moisture and soil.
You can change out the brush for a drill brush, cyclo or similar electric powered scrubber. You can still use a towel.
Sprayer can be upgraded to handheld pumpup or electric sprayer at some point.
You could upgrade to a Vonschrader upholstery machine which applies a foam, scrubs and sucks. You can still follow with a towel.
The above methods would be considered low moisture which is similar to what you're used to using for carpet.
Hot water extraction is popular but the equipment will cost more. Used will cost less. A small portable like the Cross American Quicksteam or Mitey One should do the trick. You can still scrub then follow up with hot water. You can still us a towel.
Notice the towel part?

Follow with an application of protector if the customer is happy with the cleaning. This can be applied with a hand sprayer or electric.
Next you could add a fan to speed dry everything.
Products?...........There are numerous quality product lines available. Vacaway, CCS, Fabpro, Releasit, Cross American are just a few great sources. We have links to most in our LINKS section. The tab is at the top of every page.
Are there any distributors near you? They can be a great source of info when you're starting out too.
Another thing you will want to learn is fabric identification. If you stick with a neutral or acidic side (ph less than 7) you should be good to go with most upholstery. There are exceptions. That's why its good to know what you are dealing with.
By the way..........Welcome to the board! Looking forward to reading your posts.
