I believe that the most humane way you can get your meat is, in many places, to hunt for it. Because humans have reduced habitats and/or eliminated other predators in many places, wildlife management agencies have to use human hunting as a tool to keep populations at sustainable levels.
Example: if there is enough food in a given area for 100 deer to survive the winter, but there are 200 deer, that doesn't mean that half of the deer will starve to death before spring--it means that all of them will eat quite well for the first half of the winter, after which food will become extremely scarce and most of them will starve to death.
Wildlife management agencies constantly monitor population levels in order to determine how much of the population needs to be culled each season in order for the remainder to survive. Bag limits or tag quotas are set accordingly. I currently live in a place with so much deer overpopulation that local hunters never kill enough each fall, so professional hunters have to be hired each year to get the herds down to a sustainable size.
If you hunt with respect for your game and only take shots which are likely to be clean, you will give your kill a quick death instead of a very likely slow and painful death by starvation. Also, the life it would have lived up until that moment would have been about as humane as possible.
No matter how well a farmer treats his cattle or chickens, the fact is that they were raised for the express purpose of being slaughtered. Wild game is a natural part of the ecosystem that is only killed out of necessity to keep that system in balance. Either way, an animal is dying so that you can eat.
I certainly enjoy beef, chicken, lamb, and other farm-raised animals, and eat far more of those than of things I've killed myself. I also realize that many people simply would not want to hunt. However, for any who have never tried it, and who are looking for ways to make their meat consumption more humane and ethical, they should consider giving it a try.