Wipe the stain off with a clean, damp cloth. Keep rubbing the area until it is damp, but not soaked through.
Apply some cleaning solution to the soft cloth. You can use a store-bought leather bag cleaner, which often comes in a kit. You can also make your own by mixing a few drops of a mild soap (such as unscented dishwashing soap or baby soap) with distilled water.
Wipe the stained area again with the soft cloth until the stain is gone. Try to keep your stroking motions in line with the leather's grain. This will help protect the integrity of the leather.
Use a clean, dry cloth to wipe off any soap residue or excess moisture. Don't worry about drying the bag just yet.
Let the bag dry for about 30 minutes. Avoid speeding the process up with a hairdryer. If you are in a hurry, consider setting the bag down in front of a fan. Cool air will be less damaging to the bag than hot.
Apply some leather moisturizer to the bag once it is dry. Use a soft cloth to apply the moisturizer. Rub the moisturizer on using circular motions. The moisturizer will help keep the leather soft and supple. Do not substitute regular hand lotion, which can stain and degrade leather.
Consider buffing the leather with a dry cloth. This will help restore the texture and shine to the bag.