First off, you need to know the names of the animals, then everything comes easy - the names of the meats are derived straight from them and are not borrowed from a different language. Even the shop is called "mesara"
- svinja - svinjetina (or svinjsko meso) - swine - pork (or swine meat). If you were visiting churches, you may have noticed that "sv." means "st." - then you see the same abbr. in a mesara - don't get confused, it's short for svinjsko. One of the few times when you need context to understand.
- prase - prasetina (or praseće meso) - piglet('s meat). The culture praises this above ordinary pork; there can't be a proper wedding or doček without a piglet on the spit (funeral as well).
- ovca - ovčetina (ovčije meso) - sheep - mutton
- jagnje - jagnjetina (jagnjeće) - lamb (and I couldn't find the name of the meat in english, probably lamb again)
- govedo - govedina (goveđe) - irregular; govedo is a general name for cows and bulls together; cow - beef
- june/junica - junetina (juneće) - heifer (female or male) and the meet thereof
- tele - teletina (teleće) - calf - veal
- koza - kozetina (kozije) - goat
- jare - jaretina (jareće) - kid (and the english name of the meat would be kid again, I guess - my dictionaries and my diet left this out)
With birds and fish it gets more complicated, as the fish meats don't get named (only som-somovina, catfish and perhaps a couple of other luminaries) and for poultry there's such a confusion that any anlophone person should feel at home. "Kokoš" is the word for hens, roosters and chicken; kokošije meso, however, is only of the first two. The chick, pile - piletina, pileće meso. As soon as they start laying eggs or humping the hens, they aren't chicken (which creates a lot of confusion when translating "chicken soup" - why would anyone put young meat in the soup, for that you need older).
Then there's "živina" and "živinsko meso" - no separate word for the meat except just "živinsko" - but while živina means poultry in general, including turkeys, geese, ducks and a few rarer kinds, "živinsko" is actually hens and roosters, not any of
- ćurka/ćuran, ćuretina, ćureće - turkey
- patka/patak, pačetina, pačije - duck
- guska/gusan, guščetina, guščije - goose
Few oddball cases:
- rak, račetina, račije meso - crab
- srna, srnetina, srneće meso - venison
- krmak, krmetina, krmeće meso - boar (including wild)