So I'll walk you through my thought process for determining acidity.
First off, when you are an analyzing if a molecule is going to be acidic, what you need to do is look at the conjugate base and decide, is the conjugate base going to be stable? If the conjugate base is stabilized, it means the acid is going to be more acidic. The challenge problem says, hint look at the conjugate base, but that's more universal.
I consider four factors, which if I recall I mainly learned from Klein's Organic as a Second language books.
1) When looking at the conjugate base, what atom are you stripping the proton? For example, water - if water loses a proton the negative charge is left on an oxygen atom. That's decent. If you strip a proton from methane though, negative charge is left on a carbon, that's terrible.
The trend is more electronegative - more stable. Larger - more stable.
This trend is very easy to see when you look at HCl, HBr and HI. HCl is less acidic than HBr is less acidic than HI. Why? Because if we look at the conjugate bases we see Iodide is larger than Bromide is larger than chloride, and can therefore, stabilize the charge better.
2) Resonance. Resonance stabilizes molecules. If the conjugate base has a significant resonance contributor, the acid is more acidic.
3) Induction. This one is also fairly intuitive. A proton is a little ball of positive charge. The more negative charge, the more attracted that proton is going to be to it. Induction is when a more electronegative atom or group pulls electrons from a less electronegative atom. If a group is pulling electrons away, there is less negative charge attracting the proton and it is therefore, more acidic.
4) Hybridization. sp is more acidic than sp2 is more acidic than sp3. There are a few ways people look at this. Here's how I think of it. S orbitals are lower in energy than p orbitals and are therefore more stable. An sp orbital has more s character than an sp2 orbital or an sp2 orbital and is therefore lower in energy than sp2 or sp3 orbitals and thereby makes the acid more acidic.
Hope I helped.