Clean well with a glycerine saddle soap, spray or bar. Wipe it down after you clean one area (to remove the suds). Once it's all clean, clean it again
. Use a soft or medium tooth brush to get in the crevices and tooling.
Let it dry, then condition it. I prefer Hydrophane Leather Dressing, $15 from Dover. It softens and restore leather, and waterproofs it. It's an oil based conditioner. Use a sponge or cloth and give it a liberal coat. If it soaks it up right away, give it another coat. Let the saddle dry for 24 hours. If the leather still feels too dry, condition it one more time.
Be sure to clean and condition all available leather surfaces, front and back. Use a suede or nubuck cleaner if it has a suede seat.
For the last three days I have been cleaning tack, lol. We just bought a house and moved the horses in. A lot of my tack got moldy from the last two hurricanes that came through (the barn got flooded). I've cleaned 6 bridles, two leather halters, 2 leather girths, an English saddle, 3 western saddles, an old McClellan saddle, a treeless Bob Marshall endurance saddle, and a partridge in a pear tree, LMAO. I still have another pile of tack and three more saddles to clean... Acckkkk! Some of the mold was scary technicolor. I've never seen orange mold before... lol Anyway, it all got cleaned with glycerine soap and Hydrophane. My can of Hydrophane is still half full, after all that and having it for 6 months prior. A little goes a long way!