Long and short vowel sounds actually refer to the different ways, lengths, or extent to which a vowel sound is produced. In English, while dealing with phonetics, we actually have three different kinds of vowel sounds, which are monophthongs, diphthongs, and triphthongs. Monophthongs are just single letter-sound, while diphthongs are double, and triphthongs are triple. Now, have this cleared in your mind that all diphthongs and triphthongs are long vowel sounds.
Talking about the monophthongs, they consist of both short and long vowel sounds, but they are easy to differentiate. In written form, the long sounds have a colon sign (:) in their front, whereas the short vowels do not have. When it comes to pronunciation, the short vowel sounds are produced shortly and sharply, while the long vowel sounds take relatively a long time and produced in vibrating manner. Make reference to your English or phonetic textbooks with the explanation made above, and see how accurate and easy it is.