I have used different products, but I like the Leather New, Pure Neatsfoot Oil(not the compound), Murphy's Oil Soap or Olive Oil. If you have a concern about the product changing the color of your leather I would suggest a patch test first.
I use the air compressor and a soft natural bristle brush and get all the dirt off I can. Then depending on what I am using I will use a soap to clean the saddle using a rag and a toothbrush for the tooling to clean it. Wipe it down with a clean rag.
For conditioning I set it in the house or out in the sun to warm up and open the pores and give it a good wipe down with a rag soaked with a conditioner.
Everyone does it different but that's how I do it :)
I DON'T LEAD 'EM AND FEED 'EM, I RIDE 'EM AND SLIDE 'EM.