Driving Solenoids from Arduino
You can drive the solenoid using only the MOSFET (or a bipolar transistor)
It would help to know what type of solenoid you wish to drive so we can select suitable components. Here are a couple of circuits to give you the general idea for MOSFET/Bipolar:



The resistor can be ~10k - 100k (the range can be wider as Steven notes, e.g. 1k\$ \Omega \$ - 10M\$ \Omega \$ - too high a resistance and you risk susceptibility to noise though), it's to make sure the gate is pulled to ground if the input is floating. The diode can be almost any general purpose diode capable of handling a reasonable amount of current.

Darlington Version: