How does capacitor block DC when an AC signal is superimposed on top of it?
One good way to look at this is as complex impedances. The resistor has an impedance of R, no matter what the signal frequency. The capacitor, on the other hand, has an impedance of \$\frac{1}{2\pi f C} \$. So you have a voltage source in series with two impedances; it's a voltage divider, and all the usual rules apply. The voltage that appears across the resistor is:

\$V_o = V_i\frac{R}{R+\frac{1}{2\pi f C}} \$

The other important thing to realize is that you can split your voltage source into two; you have one DC 10V source, and another AC source. The two do not impact each other, so you can pretend they're actually separate circuits. Just analyze each circuit separately, and add the results.

The DC analysis is simple. DC is zero frequency, so the capacitor has infinite impedance. You end up with no voltage across the resistor, and full DC voltage across the capacitor.

The AC analysis depends entirely on the capacitance and the frequency of the AC signal, which you don't specify.