Let's break the formula up into three potassium ions, one chromium ion, and three oxalate ions. Then we can assign the oxidation numbers to each of the three potassium ions (+1), and each of the three oxalate ions (-2), and then calculate the charge on the chromium ion, so that the sum of all the oxidation numbers would add up to zero.
K = +1, K = +1, K = +1; Sum = +3
C2O4 = -2, C2O4 = -2, C2O4 = -2; Sum = -6
Cr = +3
Total charge = +3 -6 +3 = 0
Answer: The oxidation state of the transition metal in K3[Cr(C2O4)3] is +3.