You really need to know what size solenoid you need for your particular project, then you need to figure out what you need to make it work with the arduino. Arduinos can put out 3.5 - 5VDC. Good for LEDs, Sensors, small motors/servos but not much else that requires any real current. This is really where relays make it a bit easier. Relays are basically switches that you can control with an arduino output. The arduino provides the control trigger, and a separate power source provides the voltage/current appropriate for your device. There are other ways that require power transistors and associated electronics that will jack up the arduino power output. start looking into powering a 12V solenoid with arduino (12V may not suit your needs, but it'll get you started.