In a series circuit there is only one loop, so the current is the same at every point. The potential differences across the components add up to the potential difference of the supply, because the energy from the cell is shared between them. The total resistance is the sum of the individual resistances.
Worked example: a 12 V cell is connected to a 4 Ω resistor and an 8 Ω resistor in series. The total resistance is 4 + 8 = 12 Ω. The current is I = V ÷ R = 12 ÷ 12 = 1 A, and this same current flows through both resistors. The potential difference across the 4 Ω resistor is V = 1 × 4 = 4 V. Across the 8 Ω resistor it is V = 1 × 8 = 8 V. Check: 4 V + 8 V = 12 V, which is the supply. In the same way, a 0.5 A current in a 6 Ω resistor gives V = 0.5 × 6 = 3 V, and a 9 V supply minus 3 V leaves 6 V for the other component.
To solve a series problem, find the total resistance by adding, use V = I × R to find the current, then use V = I × R again for each component. If the current and the potential difference across one component are known, subtract from the supply to get the potential difference across the other one.