One of the places where NMR spectra are nicely predictable is on the aromatic protons of simply substituted aromatic systems. Tables like this one
http://www.chemistry.ccsu.edu/glagovich/teaching/316/nmr/1hpredictbenzene.html were once very useful before software NMR predictors were incorporated into almost every chemical utility.
In short, the protons on a benzene ring are located so far downfield (7.27 for unsubstituted benzene, compared to 1.43 for cyclohexane and 5.66 for the alkene protons on cyclohexene) because of the anisotropy caused by the ring current. When electron density is pushed into, or pulled out of the aromatic ring, it changes the ring current. Substituents on the ring can be electron withdrawing or electron donating, but their effects are not the same at every point in the benzene ring - whatever the effect is, it is most strongly felt at the ortho and para positions of the substituent, due to resonance effects. A table like the one referenced above tells you how much effect an substituent will have on the chemical shift of a proton on the ring.
In your example, you have a ketone in the meta position to H2 and a methoxy group in the ortho position to H2. From the chart, a ketone in the meta position will raise the chemical shift by 0.14, and a methoxy in the para position will lower the chemical shift by 0.48. The actual chemical shift should be around 6.93.
For H1, the effect from the (now ortho) ketone is much stronger (+0.62) and from the (now meta) methoxy much weaker (-0.09) - the actual chemical shift should be around 7.80.
So in general, electron withdrawing groups like ketones, acids, esters,and nitro groups will raise the chemical shift of protons on the ring, and most strongly in the ortho and para positions. Electron donating groups like hydroxy, methoxy, and amine will lower the chemical shift of protons on the ring, again, most strongly in the ortho and para positions.
This is very general - if you look at the chart you will note some variation especially in the ortho positions, where you can also get neighboring group effects from the fact that the ortho substituent is so close in space.