Schwa is the name given by linguists to /ə/, the commonest vowel sound in English - the unstressed weak vowel heard in the usual native pronunciation of 'the', in natural; speech; to students of phonetics, the 'mid-central vowel'. If you want to hear it, say 'The President of the United States' as naturally as you can. You should hear a schwa in the middle of this - in both 'the's. The schwa is easily confused with /ɜ/, the 'open-mid central un- [or slightly]-rounded vowel' - both are produced very centrally in the mouth, and both are very relaxed.
The symbol for a schwa in the IPA is /ə/. (The word schwa is of course also used as a name for this symbol, which printers call a 'turned e', ə.)
schwa is pronounced very like 'shah' with a '-w-' inserted, IPA: /ʃwɑː/.
The schwa can be represented in writing, in the normal English alphabet, by all five of the regular vowels: a (as in 'usual', 'burglar'), e ('the'', adviser' and 'centre'), o ('pastoral' and 'doctor') and u ('occur' and 'sulphur').