ABLATIVE ABSOLUTE
You may have noticed that there is no past active participle in Latin, no word for having left etc. Partly to get around this absence, Latin has its own unique construction, the ablative absolute. Look for a group of words all in the ablative. They will often include a participle, and they will often be at the start of a sentence. Translate the ablative absolute as literally as possible first, then more idiomatically.
The ablative absolute will give you some information about circumstance, but it will always be cut off grammatically from the main sentence: think of it as a self-contained unit. Remember that the tense of the participle will be relative to the main verb, and that sometimes there may be no verb or participle at all. carminibus cantatis, discesserunt (“When the songs had been sung, they left”); me duce (“With me as leader …”).