Based on their molecular structure, how can you figure out which is stronger between two oxyacids? Our textbook is really vague. I thought it had to do with which had more oxygen but one of the question compares CH3COOH and CCl3COOH so now I'm lost again.

It does have to do with the number of oxygen atoms for H2SO3, H2SO4 and that class (HClO4, HClO3, HClO2, HClO)but there are many different classes to deal with. The one you have here is called the inductive effect. When highly electronegative atoms are placed on a carbon atom that is very close to the COOH group, the F, Cl, etc withdraws electrons from the COOH group resonance and the proton is more easily ionized. So the acid strengths go CH3COOH < FCH2COOH < F2CHCOOH < F3CCOOH.