What is an ablative absolute? How can they be translated?

An ablative absolute is phrase consisting of a noun or pronoun in the ablative, and a participle (present, future, or perfect) agreeing in case (ablative), gender (masc., fem., or neut.) and number (sg. or pl.). The phrase is a subordinate clause grammatically separate from the rest of the sentence.
There are a variety of ways in which an ablative absolute phrase can be translated.Sometimes a literal translation is appropriate. e.g. equites duce spectante oppidum oppugnaverunt With the general watching, the cavalry attacked the townMore commonly, the phrase is translated as a clause. Temporal clauses are most common: e.g. urbe captura omnes cives fleverunt literally With the city about to be captured, all the citizens cried idiomatically When the city was about to be captured, all the citizens criedSometimes, when the perfect passive participle is used, the ablative absolute phrase can be translated into the active. e.g. luce viso Caesar in portum navigavit literally When the light had been seen, Caesar sailed into the harbour idiomatically When Caesar had seen the light, he sailed into the harbourThis translation is acceptable because it is natural to assume that Caesar, as the subject of the main clause, is also the one who saw the light, rather than someone else.The verb esse has no present participle, so when translated into English, "being" has to be supplied, as there is no actual participle in the phrase. e.g. Mithridates rex Ponticus Pompeio duce victus est literally With Pompey being general, Mithridates the king of Pontus was conquered idiomatically With Pompey as general/Under Pompey's generalship, Mithridates the king of Pontus was conquered