Mint marks are cool! They allow you to figure out in what city your coins were made. Roman mints beginning in the later years of the 3rd century AD ( 270 AD) started to use these marks, which became regular from the time of Diocletian, late in that century.
Mint marks are almost always found at the very bottom of the reverse of the coin, in what is called the exergue. This might be separated by a line from the field, or not. Sometimes however they might be located between the little figures standing on the reverse; often of the emperor and Jupiter, Sun, or another god.
The mint marks usually contained the first few letters of the city, but different abbreviations were used. Hence, on some coins we may see only one letter, like A, while on others three or four letters, like ARL, both from the same city, Arelatum. There is some confusion sometimes however, because the same letter may be used for two different cites, or in one case it can stand for the workshop (with the city not indicated), and another just the city (with the workshop not indicated). In such cases more advanced knowledge such as the style of the coin is required to identify the mint correctly, or you may have to resort to the RIC catalog.
This is also the case for coins from a time before mint marks were used at all, however, some emperors only struck in certain cities, during some times only certain mints operated, or some mints only struck in a given metal. Literature will help a lot in identifying where most coins were made, and with time one can start to remember some of the information.
The mints were spread all the way from England to Asia Minor and Africa. However, not all of them were operational all at once, and some were only open for short periods of time or under only one emperor. The larger ones however were in use for a long time. If you search the web, you will be able to find pictures of Roman architecture and historical information for many of the cities where your coins were minted. Look for example into places like Arles in France, Carthage in N. Africa, London in England or Trier in Germany.