What you need here is a join.
A normal left join works like this:
LEFT JOIN [name of table] [name of table you will want to use]
ON ([where statements searching for the right columns to join])
So your query will look something like this:
SELECT a.aID, a.aName
FROM `connections` c
LEFT JOIN `author` a ON (c.cActorID=a.aID)
WHERE c.cVideoID=[id of the video]
Now first of all you say the database you want to catch the columns aID and aName from the table a next you use the FROM statement to "import" the connections table as "c". You then load the author table and make it accessible as "a" (see the select statement a.[...]) and you also say that it should join the two tables ON every c.cActorID=a.aID and in the end you make a where statement to declare you are only searching for videos with the c.cVideoId=[id]