tell me, how am I supposed to know that they'll be hydrated
All ions in water solutions are hydrated. And you are supposed to know such things - you are studying chemistry, aren't you?
But it is not relevant for this question.
Can you tell me how knowing the ions will help me learn to write these equations? And where can I find a list or something of these ions?
I don't think there is such thing as a list of ions - but you should be probably able to find simple rules that describe how to find their charges.
How they will help you? You know AgCl precipitated from the solution, you just remove these preciptated ions (Ag+
) from the list - and you are left with other ions, they form a salt - NaNO3