Is this the most common way to phrase this in Russian? As opposed to, say, "где могу найти"?
Yes, it's the dative case of я (to me) with the omitted predicative можно (one can): "Где мне (можно) найти мясо?". Literally:
- Where can I find meat?
It's difficult to say which variant is more common, "Где мне найти" or "Где я могу найти".
You could ask for “this meat” (like when showing a photo of a particular kind of meat) by «это мясо», but lacking definite articles, there is no (semantic) difference between “meat” and “the meat” in general respectively.
It's a common usage in American English to ask where the meat is when speaking either specifically or generally, e.g.,
1. You're assigned by the head of the household to cook the meat for dinner. When it comes time to cook, you ask, "Where is the meat?"
2. You go to a supermarket you've never been to before, and you're in a hurry because you're supposed to cook the meat tonight. You approach an employee and ask, "Where is the meat?", which means "Where is the meat department in this gigantic store?"
You'd always use "the meat", not "meat" without the article.
"Where do I find meat?" is so over-broad and vague, it is unacceptable English, either formal or colloquial.
Yes, but there are other contexts, like "where can I buy meat?" as in where is a store where meat is sold, where you definitely do not use the article.