Types of circuit
In a series circuit, the flow of charge only has one path to follow.

The current $$I$$ in a series circuit is equal at every point in the circuit ($$I=I_{1}=I_{2}=I_{3}=...$$).
In a single water pipe, the amount of water passing though the pipe is the same at every point.

The total potential difference $$V$$ across all of the components is the sum of the potential difference across each individual component (i.e. $$V=V_{1}+V_{2}+V_{3}+...$$).

The total (effective) resistance $$R$$ is the sum of the resistances of each individual component (i.e. $$R=R_{1}+R_{2}+R_{3}+...$$).
In a parallel circuit, the flow of charge can take two or more different paths because the circuit is split into different branches.

The current $$I$$ in the main branch (the one containing the battery) of a parallel circuit is equal to the sum of the currents of individual branches which are connected to it. $$$I=I_{1}+I_{2}$$$

The total voltage $$V$$ across all of the components is equal to the voltage across each component. $$$V=V_{1}=V_{2}$$$

The reciprocal of the total (effective) resistance $$1/R$$ is the sum of the reciprocals of the resistances of each individual component. $$$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$$$
As you add more branches with more resistance, the overall (effective) resistance of the circuit decreases.
More often than not, circuits are composed of both series and parallel sections. The rules that apply for pure parallel and pure series circuits also apply to those portions of the circuit that are connected in parallel or in series respectively.
You must simply determine which sections are in series and which are in parallel.
For example, to determine the resistance of two parallel resistors connected in series to another resistor, first apply the resistance formula $$1/R=1/R_{1}+1/R_{2}$$ to determine the equivalent resistance of the parallel resistors.
Next, apply the formula $$R=R_{1}+R{_2}$$ to the series resistor and the equivalent resistance of the parallel resistors.
The same principle applies to the other formulae for series and parallel circuits.