Take your rug outside and shake it out--this is a fast way to get rid of loose dust that's gathered on it due to foot traffic or miscellaneous loose dust in the room. Once you've done that, bring the rug inside.
Mix water and a mild, natural soap into a bowl or a bucket, depending on the size of your rug. If the manufacturer of the leather doesn't recommend cleaning with soap and water, use a foam-based leather cleaner.
Dip a rag into the cleaning mixture and wipe softly in a circular pattern.
Wipe away any excess residue from the soap or foam with a second rag dipped in clean water and wrung for excess moisture.
Blot the rug dry using soft towels weighed down with heavy objects. A book will do the job nicely. This will reduce the possibility of scratching or color damage from any cleaner you haven't wiped away. If the rug is still moist after you've blotted it, allow it to air dry.
Apply a leather conditioner to keep the fabric supple and restore its luster.