In RP English the short vowel sounds are those in 'pet', 'pot', 'put', 'putt', 'pat' and 'pit', and the schwa sound. They can be compared with long vowel sounds.
Example
The word 'ship' has a short /i/ sound, whilst the equivalent long sound /i:/ produces the word 'sheep'.
In the classroom
Learners need practice in discriminating and producing short and long vowels. Learners who are in contact with different English accents, either in the class or outside, will hear different vowel sounds to those above, e.g. in Australian and New Zealand English.
See also:
https://www.teachingenglish.org.uk/article/long-vowels
Further links:
https://www.teachingenglish.org.uk/article/global-english-teaching-pronunciation
https://www.teachingenglish.org.uk/article/using-phonemic-chart-autonomous-learning
https://www.teachingenglish.org.uk/article/phonemic-chart