Knowing how to properly analyze an electrical circuit is necessary to calculate the measure of current and voltage through different parts of the circuit. Kirchoff's Laws are a few fundamental rules for completing a nodal analysis on any electrical circuit.
The first of Kirchoff's laws states that the sum of current flowing into a node is equal to the sum of current flowing out of that node. Let's see this applied to a very simple example.
In the above figure, the blue current is equal to the pink and orange currents combined. The second Kirchoff's law states that the sum of all voltages around an electrical circuit is zero. Let's see what this means:
In the above figure, the sum of the voltage drops across the two resistors and the capacitor is equal to the starting voltage of the battery.
The best way to learn and understand how to do circuit analysis is to see examples. Here are a few of different complexities.