I think Andy aka's circuit is exactly right, but depending on your motor, you may get away with something a bit simpler, something like this:
simulate this circuit – Schematic created using CircuitLab
If your motor needs something like 100mA you can use a small-signal general purpose NPN transistor instead of a Darlington as in the circuit above, something like BC546/547. The characteristic to look for is peak collector current: that will tell you how much of a load the transistor can drive
The diode across the motor is a snubber/flyback diode, there to protect your circuitry against harmful voltage spikes that could be generated by the motor in your pump when its is shut down. According to Andy aka (see comment below) you'll need it regardless, so in the end this might not be simpler than his circuit.
To be clear, one advantage of Andy Aka's circuit is that it is designed for any motor voltage, whereas the circuit here relies on your Arduino and the motor running off the same V source.