Sida can be both page and side, and you would really need to get from the context if you are speaking about the other side of a river or if you were talking about pages in a book.
When talking about pages "Vi är på andra sidan" would most likely be interpreted as "We are on the second page." whereas you would probably use "Vi är på den andra sidan." to mean the other page in this case and still need to have a context where it would make sense to talk about the other side as opposed to the .second side.
I'm not a native speaker, but I can answer this.
Andra - Plural / definite form. Sidan is definite, so that's the one used in this sentence.
Annan - For common gender (en words). You would use this if you said, en annan sida.
Annat - For neuter gender (ett words). You would use this if you said, for example, ett annat hus.