To calculate the voltage drop across a resistor, remember: Ohm’s Law (V=I*R) is your friend. Find the current flowing through a resistor, then multiply the current in amps by resistance in ohms to find the voltage drop in volts. A circuit having combinations of resistors in series and parallel will be more complicated to deal with, though Ohm’s Law still applies.
TL;DR (Too Long; Didn't Read)
Ohm's Law states that V=I*R, where V is voltage, I is current and R is resistance.
In a series circuit, the voltage drop across each resistor will be directly proportional to the size of the resistor.
In a parallel circuit, the voltage drop across each resistor will be the same as the power source. Ohm's Law is conserved because the value of the current flowing through each resistor is different.
In a series circuit, the total resistance in the circuit is equal to the sum of each resistor's resistance.
In a parallel circuit, the the reciprocal of the total resistance in the circuit is equal to the sum of the reciprocal value of each resistor's resistance, or 1÷Rtotal = 1÷R1 + 1÷R2 + ... +1÷Rn, where Rn is the number of resistors in the circuit.
A Simple Circuit
Simple circuits that have a single DC voltage source and a single resistor are the easiest to calculate. Although you could use Ohm's Law, you don't need it. The voltage drop across the resistor is the same as the voltage of the DC source. This comes from Kirchoff's Voltage Law, which states that all the voltages in a given circuit "loop" must add up to zero. For example, in a circuit with a 12V battery and 10K ohm resistor, the battery provides the 12V source and the resistor has a drop of 12V, adding up to zero.
Resistors in Series
Circuits with resistors in series are a little more complicated than a single resistor, but here Ohm's Law comes to the rescue, though in a slightly different arrangement. First, add up the ohm values of all the resistors in the circuit. Here, we use a little algebra to get Ohm's Law for current: I=V÷R. Divide the DC source voltage by the total resistance to get the total current in the circuit. Since the circuit is a single loop, the current is the same through all resistors. To find the voltage drop for any one of the resistors, use Ohm's Law again, V=I*R, using the resistance of the resistor you want.
Resistors in Parallel
A circuit that has only a DC voltage source and a set of resistors in parallel is easy again. The voltage drop across all the resistors is the same, and is equal to the DC source voltage. For example, put 3 resistors in parallel with a 12V battery. By Kirchoff's Voltage Law, each resistor is now its own loop. Each loop includes the battery, and the voltages add up to zero. Note that the current through each resistor is not the same, but in this case it doesn't matter.
Resistors in Series-Parallel Combinations
The picture becomes more complicated for circuits with multiple resistors in series and parallel. First, if the circuit has more than one loop, find the one in which the resistor in question belongs to. Then calculate the current through that loop using resistance formulas. If the resistor is one of several in parallel within the loop, you must find the current for the one resistor using Kirchoff's Current Law. When you've calculated the current, find the voltage drop with Ohm's Law.