Do not, I repeat, DO NOT, scrub the leather with any kind of brush, scrubber, or sponge. If you do, you will remove the top finish of the leather and it will look like crap... I made that mistake before myself, lol.
If it's really dirty, take it outside and hose it down. Use your hands to gently rub the dirt off as it loosens up. Once you have it as clean as it will get that way, get a soft sponge and some glycerine soap (I like Lexol's cleaner). GENTLY rub the soapy sponge on the leather in a circular pattern. If the suds are brown or brownish, wipe them off with a soft cloth, and clean again. Keep cleaning gently until the suds are no longer brown. Use a very soft toothbrush to get in to any tooling or crevices. Use a suede cleaner kit to clean any rough out or suede.
Let the saddle dry, indoors.
The next day, use a good conditioner like Passier Lederbalsam
or Ultra Leather Conditioner
. Put a thick coat on all surfaces of the leather, front and back. Do not use on rough out or suede. Once it's soaked in, put on another thick coat. Let the saddle dry for a day or three. If the leather is still dry in places, or all over, put another coat on. Buff with a soft cloth after the leather has dried.