For both contractions and omissions, the apostrophe replaces the missing letter.

Contraction examples would be:
   you’re for you are, where it replaces the a in are
   it’s for it is where the apostrophe replaces the i in is

Omission examples would be:
   gone fishin’ where the apostrophe replaces the g
   pot o’ gold where the apostrophe replaces the f
   rock ’n’ roll where the apostrophe replaces the a and d in and

In a date when part of the year is left out, the apostrophe needs to indicate the missing year. In the 80s would mean the temperature; In the ‘80s would mean the decade.