There are several kinds of abbreviations: shortenings, contractions, initialisms, and acronyms.
1 Shortenings of words, though formerly condemned by literary figures such as Addison and Pope (18c), are now a common convention, with varying degrees of formality (ad = advertisement, bike = bicycle, pub = public house, rhino = rhinoceros, telly = television). Some are the usual forms, with the original forms now regarded as formal or technical (bus = omnibus, fridge = refrigerator, gym = gymnasium, turps = turpentine, zoo = zoological garden).
2 Contractions are a type of shortening in which letters from the middle of the word are omitted (Dr = doctor, St = saint) and are sometimes marked as omitted by use of an apostrophe (can't = cannot, we've = we have).
3 Initialisms are abbreviations consisting of a sequence of the initial letters of words that are pronounced as separate letters: a.m., BBC, DfES [= Department for Education and Skills, in the UK], HIV, MP, UN. Practice varies as to including full points between the letters; the style recommended here is not to include them when all the initials are capitals and in some other cases. When the form has a plural, this is formed by adding an -s, now normally without an apostrophe (e.g. MPs rather than MP's). Possessives are formed in the usual way (e.g. MP's singular, MPs' plural).
4 Acronyms are initialisms that have gone one stage further and acquired the status of words, being pronounced and treated grammatically as such (Aids, laser, NATO, PIN [= personal identification number], radar). In some cases the original expansions have become irrelevant, as with laser and radar. (See more fully at acronym.)