What is humanely raised meat?
Pasture raised animals are allowed to live outdoors for a significant portion of their lives. They get fresh air, room to move around, and sunlight. By comparison, "free range" animals go outside for only short periods of time, and on some farms the outside area is just dirt or concrete, not pasture.
Note: Some farms feed supplemental grain to their pasture raised animals. If you want grain-free meat, look for "100% grass-fed" instead.
Grass-fed animals (only cows, sheep, and goats can be grass fed ) eat grass for all or part of their lives. They usually eat this grass on pasture, though sometimes (like in winter) a farmer will house them in barns and feed them hay (dried grass). My observation is that most grass-fed animals are primarily pasture raised.
Grass, by the way, is easier than grain on the tender stomachs of cattle, sheep, and goats. So grass-fed animals tend to have fewer digestive problems.
Animals don't have to be raised outdoors to have a happy life. If they're indoor animals, their lives will be greatly enhanced by the presence of "enrichments" -- objects such as perches and nest boxes (for poultry) and hay nests or wallowing pits (for pigs) that allow them to engage in natural behaviors. Think rubber balls for your dog, or laser toys for your cat -- these are enrichments.
When animals are allowed to 'be themselves' they enjoy better mental and physical health, and thus less suffering (just ask your pet).
If farm animals are being fed antibiotics, it’s usually a sign that they’re living in crowded facilities that are likely to make them sick (antibiotics prevent disease) or they're eating an unnatural diet meant to fatten them quickly (antibiotics make animals grow fast).
Antibiotics in meat is more of a human health concern than an animal welfare issue (feeding antibiotics doesn't harm animals), but when factory farms ditch antibiotics, they are forced to raise animals a little more naturally, and therefore a little more humanely. (Note: They can still crowd animals together inhumanely, without enrichments. This is why "antibiotic free" is not one of my 5 recommended labels.)
It is indeed possible for animals to be slaughtered in ways that keep pain and stress to a minimum. But it’s nearly impossible to determine how farmers and food companies slaughter their animals, because this information is never put on meat labels or packaging. (Most consumers, unfortunately, don't want to think about it, so producers don't mention it.)
If this issue is important to you, ask farmers about their slaughter facility or look for the two humane certification labels that have slaughtering protocols. (Humaneitarian is currently putting together a site page about slaughtering.)