Solubility rules are indeed problematical. I'm sad to report that you simply have to study, try to memorize, and maybe pick up a hint as you go along. For starters, look up compounds of sodium and potassium. Wikipedia isn't a bad place to look, if your textbook is lacking. You'll see, all simple compounds of sodium and potassium are soluble. And for that reason, we use them preferentially, in high school chemistry courses, in industry, in analytical chemistry.
Now, lets address your specific question, and search for hints:
A solution of silver nitrate is added to a solution of potassium bromide. I am supposed to write the equation out and include phases.
AgNO3 + KBr --> AgBr + KNO3
You found your first hint, the reactants are solutions, so they're (aq). That means they're not really there -- they exist as Ag+(aq), NO3-(aq), K+(aq) and Br-(aq). Now what, if they all stayed as solvated ions, how can there be a reaction? Something has to happen, somewhere in the products to drive the reaction forward. An insoluble solid is just the ticket. So is a gas bubbling away. But what happens? And to which one?
I sort of understand solubility rules now. NaOH would be soluble because all group 1a metals are soluble. Ammonium basically makes the entire compound soluble as well. There are still a few loopholes to these rules I don't understand. CaF for example. None of those elements are on my solubility chart or anyones I can find on the internet. I assume that when there are no rules regarding its solubility, it is simply insoluble.
I guess with the states, you just have to memorize them. Obviously Oxygen and Carbon are going to be gases. Water is the only liquid I've encountered in doing these problems. Others are either aqueous or solid and this is determined by solubility rules.
@enthalpy I am trying to grasp what you're trying to say to me. Essentially, you're saying that for two aqueous solutions to react, the ions that switch must form an insoluble compound as a product? I believe this is similar to what @Arkcon was trying to tell me. In order for a reaction to happen one of the end products must be solid. I vaguely remember learning about this in chemistry class. Something about a precipitate? I wish I could ask my teacher but it is still summer and he won't respond to any emails.
I'm looking over my entire page of problems ad I'm kind of noticing a pattern. Almost all of my reactions have a solid and an aqueous solution! Please correct me if I'm wrong but thats what I'm getting from you guys.
As always however, there were exceptions to this rule I found.
BaCl2 + 2Fe(NO3)2 --> Ba(NO3)2 + FeCl2
I balanced the equation on my paper but lets ignore that for now and focus on the states of everything in this reaction.
First two are aqueous. Barium Nitrate is aqeuous because nitrate is always soluble. Personally, I believe that the second compound is aqueous. However, if what I'm getting from you guys is correct, it should be solid right? It would be pointless for all reactants and products to be soluble like @Enthalpy said.
I get the general idea of what you guys are saying. Just don't understand why there are exceptions and why they exist.