It actually isn't as much hocus-pocus as it seems like when you watch the teacher doing the examples on the board. There really are rules you can follow. You do have to know the 5 reactions types first, or you won't be able to get anywhere. Luckily I have already covered that and you can check it out if you need review. Reaction Types, or "What's Going On?" and How Could I Forget Combustion??
So if you start with 2 single elements, it is synthesis and the product will be a simple ionic compound made of those elements. You put the positive one first and use the charges to figure out the subscripts in the formula.
If you start with 1 compound, it is decomposition and the products are the two elements that made up the compound. Remember that diatomic elements get a little subscript 2 when they are alone.
If you start with 1 compound and one element you have a single replacement reaction. If the element is a metal it will switch places with the metal in the compound. If the element is a nonmetal it will switch places with the nonmetal in the compound. You need to check the activity series to see if the reaction will happen. If the element is more reactive (higher on the list) that what it will switch with in the compound the reaction will happen. If it is less reactive the reaction will not happen. (The "No Reaction" ones are easy because you don't have to figure out any formulas or balance anything)
If you start with 2 compounds, it is a double replacement and you will switch the two metals. Each metal will pair up with the other nonmetal or polyatomic ion.
Whenever you make a compound you need to look at the charges to make sure you get the correct formulas.
If you start with a hydrocarbon (something with just hydrogen and carbon) plus oxygen, it is combustion and the products will always be carbon dioxide and water.
So, figure out what type of reaction it is and follow the rules to figure out you will get for products.