What are the possible charges for ions for the following elements?

In the spirit of not doing it all for you, let me say that Na, Ba, Ga, and Mg are completely straightforward ? just look at the groups these elements are in and you should be able to work out their oxidation states.  (Well, Ga might give you a little pause, but gallium's chemistry is similar to aluminum - right above it in the periodic table.)

Cu, Zn, and Mn are a little more challenging, but I find it hard to believe that you "can't find it anywhere".  Try Wikipedia or your textbook.  If I use either the Yahoo search engine or Google's and I search "Copper compounds wikipedia" I get a lot of Cu compounds in a long list - most of them have the same oxidation state.  I'm sure that Zn will be even more clear.  Now, manganese is the only one that requires some experience - so my hint is that Mn is quite stable with a half-filled 3d shell (and the 4s electrons ionized away).  EDIT: "You've Got Dangled" (Jeremy), the Mn³? oxidation state is not what I was hinting at and it is not particularly stable in aqueous solutions.

Zn2+
Mg+
Cu2+ or 3+
Mn3+ or 7+

A. Na2SO4
B. Ba3(PO4)2
C. Ga2(SO4)3

To find the charges of these ions, simply search anywhere: Zn ion or Ga ion or Mn ion, etc.

You mean the valence electrons of the elements.  Just simply call it the valence of an element so you will not be confused.  Refer to the Periodic Table or the Periodic Classification of the Elements.  If you have already studied the Electronic Configurations of the Atoms of the Elements, the valence is in the outer shell and probably the highest sub-level. For example, Ba has two electrons at the 5f.
Valences (Charges as you call it):
Zn = +2
Mg = +2
Cu = +1 (Cuprous), +2 (Cupric)
Mn = +2 (Manganese) - Please watch your spelling
For compounds made up of two elements,
The subscript of a positively charged element is the valence of the negatively charge element and vice-versa.
Remember this:
You just "criss-cross" the valences or exchange them. Exchange the valences, so to speak.
For compounds made up of positively charged element and negatively charged radical (for example SO4^-2 = negatively charged all the time) the subscript for the element is the valence of the radical while the subscript of the radical is the valence of the element.
(Element^+V + Radical^-V) = (Element subscript -V)(Radical subscript +V
)
In these problems the elements have positive valences while the radicals have negative valences.
For A.
Na = +1
SO4 = -2
Hence:
Na-2(SO4)+1
or Na2SO4
For B:
Ba = +2
PO4 = -3
Ba3(PO4)2
For C:
Ga = +3
SO4 = -2
Ga2(SO4)3
Please study the mechanics above and you will master this technique for the rest of your course in Writing Formulas.
TIP:  
You should memorize these "charges" and the best way is by referring to the periodic table.
For example (+1)
Group Ia;
H, Li, Na (Natrium), K (Kalium), Rb, Cs, Fr
Group Ib;
Cu (Cuprum), Ag (Agrum), Au (Aurum)
For example (+2):
Group IIa;
Be, Mg, Ca, Sr, Ba, Ra
Group IIb;
Zn, Cd, Hg (Hydrargyrum)
For example (+3)
Group IIIa;
Sc, Y, La, Ac
Group IIIb;
B, Al, Ga, in, Tl
Radicals:
NO3 = -1
SO4 = -2
PO4 = -3.
Here are bonuses for your further study:
Sodium Nitrate = Na(NO3) or NaNO3
Barium Chloride = BaCl2
Barium Sulfate = BaSO4
Aluminum Nitrate = Al(NO3)3
Aluminum Sulfate = Al2(SO4)3
Aluminum Phosphate = Al(PO4) or AlPO4
Sodium Nitrate = Na(NO3) or NaNO3
Hint:
When both valences are equal there will be no subscripts.
Please email me if you have further questions.
Good Luck !!!!

Zn2+

Mg+

Cu2+ or 3+

Mn3+ or 7+

To fill in the blanks, find the charge of both the ions then criss-cross them ( in other words; put the charge on each ion on the opposite ion and if you can then reduce ).

A. Na2SO4

B. Ba3(PO4)2

C. Ga2(SO4)3