The legend is obviously a vital aid to identifying a coin but in many instances parts of it are missing. Below is a brief list of the more commonly used obverse inscriptions on coins found in the UK which might help when you're trying to fill in the gaps.
AVG:
Augustus, the title taken by senior emperors (Augusta for empresses)
C/CAE/CAES
Caesar. Emperors held both Caesar and Augustus as titles until late in the Empire, when Caesar was used only by junior emperors or heirs to the "throne". A senior emperor could use Caesar amongst his titles but a junior emperor could not use Augustus.
COS
Consul. Often followed by a number to denote how many times the emperor has been declared consul.
DIVO/DIVA
Used on commemorative coins to denote that the emperor/empress has been deified.
DN
Dominus Noster. Our lord.
IMP
Imperator. It means "commander in chief of the army" rather than "emperor"'.
IVN
Junior. You'll only find this on coins of Licinius II and Constantine II and it's very useful for distinguishing the coins of father and son.
MAX
Maximus. Greatest.
NOB
Nobilissimus. Most noble
PM/PONT MAX
Pontifex Maximus. Chief priest. Used by the senior Augustus if more than one, with Pontifex used by the junior.
PF
Pius Felix. Pious to the gods and blessed by them.
PERP
Perpetuus. Forever.
PP
Pater Patriae. Father of the country.
TRP
Tribunicia Potestas. Power of the Tribune, also often followed by a number denoting the number of times the office was re-affirmed.
There are others but those should see you through the vast majority of coins found here. But one other aspect is worth mentioning, namely legend relating to family, such as:
FL
Flavius. The Flavian emperors were Vespasian, Titus and Domitian
But beware of some family names which will appear on various emperors' coins. Examples are:
M AVR/AVREL
Could be Marcus Aurelius but these abbreviations appear on numerous rulers' coins. Also:
ANTONINVS PIVS
It could be the obvious (Antoninus Pius) or it could be Elagabalus or Caracalla.
A great site for seeking out possible issuers of worn/damaged coins that have lost some legend is romancoin.info which has instructions on how to enter the surviving legend and which will then give you a list of candidates.
I'd also highly recommend A History of Roman Coinage in Britain by Sam Moorhead
