The surface of most gloves can be spot cleaned simply by gently rubbing the soiled area with a solution of Woolite, and water. (Follow manufacturer’s directions).
Fabric gloves, even with leather palms, can be hand washed with sports wash or Woolite. (Follow manufactures directions). Be sure to rinse thoroughly to remove all detergent. It is a good idea to have your hands inside your gloves during the wash & rinse process to help maintain the shape of the gloves. Soap has surfactants that reduce the surface tension of water and dramatically reduce waterproofness. (Nikwax or a similar waterproofing material, works best). Be sure never to wring out your gloves, it will ruin the internal stitching and lining materials. You need to let the gloves air dry away from direct heat.
Clean the outside of leather gloves with a mild leather cleaner. It is recommended that you have your hand inside your glove as you gently clean it. After cleaning, you should spray your gloves with a silicone spray to protect the leather. As for the inside of the glove: it is very difficult to clean the inside of gloves. You could try using Woolite on a cloth and gently clean the inside or try spraying the inside with Febreze. Then you would have to let them air dry.
A second option is to have your gloves professionally cleaned.