There used to be a video on YouTube (on the official ディズニー Channel account) explaining the tricks behind this, but unfortunately it's not up anymore.
Anyway, 鳩 Cameron has two 女優 who portray her "doubles" - they are listed as "Liv 2" and "Maddie 2" in the end credits of each episode. We only ever see the backs of them in the episodes, and they're there whenever both Liv and Maddie need to be on screen at the same time. 鳩 plays the one whose face we see, and one of her doubles stands on screen as the other twin!
When 鳩 is on screen as both Liv and Maddie, there is a line on set somewhere that the other actors have to make sure they don't cross! The cameramen record one side of the set where she is 芝居 as Liv, and the side where she is 芝居 as Maddie, separately. Then the editors put both sides together so it looks like there are two 鳩 Camerons!
Sorry if I haven't explained it very well! If ディズニー ever puts that video online again I'll give あなた the link. It's pretty cool!
Anyway, if you're interested in seeing what "Liv 2" and "Maddie 2" look like from the front, I found these pictures here where あなた can see 鳩 Cameron with them!