These instructions will work for just about any type of meat, not just venison. Try grinding your own hamburger from a cheap steak. You will be amazed at how much better the fresh ground stuff tastes!
The first thing you need it a grinder. You don't need an expensive electric grinder, although those are nice! All you need is an inexpensive hand crank grinder. I use the "Norpro Meat Grinder, Mincer, and Pasta Maker". It only cost me $25 and is perfect for batches of less than ten pounds.
Next you need to trim most of the fat and silver skin from your venison. You can leave some on, but venison fat can have a bad flavor, so I try to get as much off as possible.
You can't put huge chunks of meat through your grinder unless you have one of those big expensive models. Cube your meat, or, better yet, cut it into strips. This will help it feed through your grinder.
Most meat grinders have a couple different grinder plates with different sized holes. These holes determine how fine the meat is ground. I prefer my venison to be ground fine, so I choose to use a plate with small holes. This is totally your personal preference.
Now all you do is turn the crank on your grinder while stuffing the meat into its hopper. Catch your ground venison in a bowl and you are done!
......Unless you plan on making hamburger patties. Most wild game does not have enough fat to keep patties from falling apart. You need to add fat to the meat to act as a yummy glue. You can use beef suet if you can find it. I just use really, really cheap bacon. Bacon that is mostly fat. This is amazingly good tasting. I like to add fat at a 10:1 ratio. Ten parts venison to one part fat. For the math challenged: for every five pounds of venison add half a pound of fat. Just mix it in real good with your hands and then form into patties.
I highly recommend you wear gloves as this is a very messy project. It is well worth the effort though, you will truly be amazed at how good fresh ground meat tastes!