You need to know the oxidation number rules and how to calculate them so that you know what is oxidized and what is reduced.
C is oxidized from +3 to +4 state and Mn is reduced from +7 to +2 state
Before you balance the half-reactions, you need to know whether the conditions are acidic or basic.
1) Write skeleton equation and balance the species undergoing Ox or Red'n: (In this case C)
H2C2O4 → 2CO2
The way that's usually taught:
2) You use H2O to balance O, which is unnecessary here.
3) Use H+ to balance H
H2C2O4 → 2CO2 + 2H+
4) Use e- to balance overall charge
H2C2O4 → 2CO2 + 2H+ + 2e-
Do the same for Mn:
MnO4- + 8H+ + 5e- → Mn2+ + 4H2O
Another process (that I prefer)
2) Use oxidation states to determine electrons needed
3) Use H+ or OH- to balance charge
4) Use H2O to balance H or O and the other must also work (It's a nice check)
In this method, you know that you know 5 e- to get Mn from +7 to +2, you need 8H+ in order to balance the charge, you need 4H2O to balance the O (and the H's are also balanced)
In order to combine the 1/2 - rxns, you make it so that the number of electrons are the same (5 x 1st rxn + 2 x 2nd reaction) which yields
5H2C2O4 + 2MnO4- + 6H+ → 10CO2 + 2Mn2+ + 8H2O
I'll leave other problems to you.