How do you figure out what IONIC formulas come about?

You just need to ensure the positive ions balance the negative ions leading to a neutral compound

1. Ca^2+ and Br^-
You have two positive charges and one negative, therefore number of negatives need doubling:
CaBr2

2. K^+ and CO3^2-
One positive charge and two negatives, therefore extra positive required:
K2CO3

3. Al^3+ and CH3OO^-
Three positives and one negative charge, so need three times the negative ion:
Al(CH3COO)3

4. NH4^+ and SO4^2-
One positive charge and two negatives, therefore extra positive required:
(NH4)2(SO4)

5. Mg^2+ and PO4^3-
The simplest way to balance two positive charges and three negative charges is to treble the number of positive ions and double the number of negative ions:
Mg3(PO4)2

You don't need 2 predict, u have 2 be sure.
     1. Ca^2 + Br^-
        just exchange the figures or find the LCM of both figures. for example, i wud just exchange
    CaBr2  or the LCM of 2 and 1 is 2, so to get Ca to 2, multiply by 1 and Br to 2 multiply by 2.
         Ca1Br2 - CaBr2.   Apply the same method for everything.
     2. K2CO3
     3. Al(CH3OO)3
     4. (NH4)2SO4
     5. Mg3(PO4)2.    
        Note, when you are multiplying to a compound a figure greater than one,you enclose the compound in a bracket cos it shows you are multiplying everything in the bracket.

Predict!? No you must know the answer!

1. CaBr2(aq)
2. K2CO3(s)
3.Al(Ch3oo)3 (aq)
4. (NH4)2 (SO4) (aq)
5. Mg3(PO4)2 (aq)