According to Pliny's "Natural History," Rome introduced its first standard circulating coins in 269 B.C. The most commonly used material was silver. For the collector, Roman coinage falls into the two broad historical categories of the Republic (from the 3rd Century to 27 B.C, when Octavius Caesar assumed supreme power and took the title "Augustus") and the Empire (27 B.C. to the 4th Century A.D.) Telling these two categories apart and identifying the most common types of coins is moderately straightforward, but achieving anything like an exact date for a coin can be a challenge.
Rule out of contention coins which bear writing in anything other than Roman capitals, any which feature a person wearing a crown or any which show the influence of the Christian cross in their design.
Check the size of the coins with an accurate measuring device such as a pair of digital calipers. A Roman coin made of gold should be no more than 24mm in diameter and no less than 1mm thick. Silver denarii are usually up to 20mm in diameter and 2mm thick, the victoriati and sestertii up to 15mm. Bronze coins up to 35mm in diameter are probably later sestertii from the Imperial era.
Examine the decoration. Coins from the Republic were often adorned with portraits of mythical or symbolic figures such as Roma, Bellona (helmeted goddess of war) and the Dioscuri (the heavenly twins). Such coins can only be given a vague date by comparing them to similar coins in a catalogue such as "Identifying Roman Coins." Imperial coinage can be dated more accurately because it usually carries a bust of the emperor or empress of the time. These are portraits of individuals rather than the idealised mythical figures of earlier periods. Usually their heads are bare or wreathed with laurels. Again you will need to search diligently before you are likely to find a match.
Female busts on Imperial coins can usually be dated from the many changes in ladies' fashion throughout that period.
Roman and Medieval coins are often confused. Medieval currency tend to be larger and thinner and will display Christian iconography.