How do you come up with the product in a combination reaction? Do the charges have something to do with the answer?

Usually, the charges do have something to do with the answer. When you balance chemical reactions, charge has to be balanced as well as the number of atoms on both sides of the equation.

Often, in ionic reactions, you will have some sort of exchange. The cations (positively-charged ions) will exchange with the anions (negatively-charged ions). For example:

NaCl + Ag(NO_3) \rightleftharpoons Na^+ + Cl^- + Ag^+ + NO_3^- \rightarrow NaNO_3 + AgCl

In this case, the driving force is the formation of AgCl, which is insoluble. Hence, the reaction is driven to the right.

Don't get too worried about the reactions. It will come in time.