Size and material description.
To describe roman coins people usually use terms like AE 16 or AU 20mm. These terms will tell you what kind of material the coin is made from and the size of the coin.
AE = bronze/copper/brass Aes in Latin means bronze
AR = silver Argentum in Latin means silver
AU or AV = gold Aurum in Latin means gold
Thus AE 18 mm would mean a bronze coin with a diameter of 18 mm. Especially for bronze coins, who can vary greatly in size, the coins can also be put into categories:
AE 1 - 25mm or greater
AE 2 - 21 - 25mm
AE 3 - 17 - 21mm
AE 4 - less than 17mm
How a coin was made.
Dies were created by carving a design into a thick bronze disk which was then fitted to an anvil. This is known as the lower, or obverse, die. The reverse die was carved at the base of a punch. Cold or heated blanks of metal were placed on the lower die, the punch was then positioned over the blank and struck using a hammer. Thus the detail of an ancient coin is referred to as a coin's strike. All the ancient coins where made this way and due to this process no two coins looked alike. It was human mass production (usually done by slaves) so lots of things could go wrong. The position of the punch could be different in position to the lower die. A die would get worn, giving much less detail to a coin, something could get stuck in either the upper or lower die thus obscuring a piece of detail. They weren't always struck with same force. The piece of metal could have been placed off center so parts of the designs would be missing. Due to all these factors every coin is unique especially in comparison with today's machine produced coins which look exactly the same.
Die alignment indicates the relative position of the obverse and reverse die.
Modern research has indicated that Roman coins were probably coated by using a mixture of different chloride salts namely silver, lead, and tin, which were all available to the ancients from mineral deposits. The salts of these metals have a melting point much lower than their pure form. The blanks would be sunk into this mixture. They remained in this mixture for a period of time during which there would be diffusion of the silver, lead and tin into the copper until the coin got a silvery appearance. The coating produced is very thin and wears off pretty quickly when used regularly. Recent experiments have been able to duplicate this coating process.
A new widely accepted explanation today is that the flans were "pickled" in a mildly acidic solution, which drew out the silver to the surface. This method has the advantage that the Romans could just mix the amount of silver they wanted into the alloy, and then they just drew it out using the acidic solution. The amount of time the flan spent in this solution determined how much of the silver content of the alloy was moved to the surface. At least from the reform of Aurelian on, this seems to have been the method used. Earlier, the chlorides method seems to have been the method of choice.
Broken or Continuous Legend.
A broken legend means that the text on the front of the coin (the obverse) is broken in two at the top, above the head of the Emperor. In case of a Caesar or junior Augustus the head would be smaller and the text would be one continuous line. The symbolism behind this is, that the senior Augustus would have a bigger portrait which would require the legend to be broken and an heir to the throne, who was lower in rank, could do with a smaller portrait with enough room to make one continuous sentence. Thus making it a sign of respect which had nothing to do with the actual room on the coin but more with symbolism.
The exergue is the place on the reverse site of the coin below the central design often used to show where the coin was minted.