How to find/mine emeralds? (Real emeralds/ read description please)?

I would like to know if it is possible to mine emeralds without being in an underground mine and the best places to look. Is a forest a good place to try and find them? How will I know if I found one? I tried looking on Google and doing research, but I got a lot of minecraft results no matter how hard I tried and what other things I typed in with my question.