We have horses, so I'm using leather gloves every day. For the most part I don't bother cleaning them.

When I do, I put on the non-insulated leather gloves and use a combination of spray-on glycerin saddle soap and water, washing them like I'd wash my hands. Fiebing's Liquid Glycerine Saddle Soap is a favored brand.

As mentioned, I let them air dry, putting them on once in a while to keep them sized and less stiff.

My current favorite gloves are:
Summer:
Wells Lamont Men’s Cowhide Full Leather Slip-On Work Gloves, Leather Work Gloves with Reinforced Palm (Wells Lamont 1130)

Winter:
Men's Heavy Duty Leather Winter Work Gloves with Thinsulate Insulation, (Wells Lamont 5127)

In winter the gloves get wet a lot. I smear Obenauf's leather preservative on the leather parts to try to keep the leather a bit drier. It's slick at first, but that fades quickly ... and it smells GREAT!!