When asked about which compound is most acidic, how can you tell?

Is it the more resonance stabilized (the more conjugated), the less acidic?

Acidity increases with increasing stability of the conjugate base (there are exceptions to this, but I doubt there will be any on a standardized test). The more freedom electrons have to move around a structure, the more stable that structure is. For this reason, resonance imparts (significant) stability. Compare ethanol and phenol. Ethanol has a pKa of about 16, while phenol has a pKa of about 10. This means phenol is 10^6 times a stronger acid than ethanol. This is because the phenoxide ion has 4 resonance structures over which to spread it's electron density, while ethoxide's negative charge is stuck on the oxygen.