There are a few different steps that can be taken in order to remove the undesirable gamey taste from your kill. One method is to remove any excess blood from your meat. By removing the excess blood you also remove a good portion of the gamey flavor. This works best on small pieces of meat, such as cubed meat for chili or small steak slices. Place your meat in a bowl of ice cold water; let it sit for 1 to 2 minutes then drain. Then fill your bowl with warm to hot tap water and let sit for 1 to 2 minutes. Repeat this process 3 or 4 times. This process causes the meat to expand and contract forcing out excess blood and therefore removing the gamey flavor.
Another option is to simply soak the meat in buttermilk, salt water or water with a little vinegar or apple cider vinegar added. Usually an over night soak is best but if you can at least get a couple hours of soak time, that will help remove some of the taste.
Be sure to remove any silver skin and fat from the meat. They hold a great deal of game flavor and its usually best to completely remove them from the meat before cooking.