Here is a handy explanation of how to use a transistor
It does say that the transistor it talks about, the BC547, is not what you want for the current drawn by a motor, but nevertheless it shows how to hook things up. It also indicates that the IRF520
is a good choice for running motors and such.
BUT..... they key thing to hooking up the motor is to use a diode as explained about half way down this page
where it shows a transistor switching a relay... mentally change the relay to your motor.
Sorry I can't help with interpreting datasheets.... I'm sure someone here will help though!
Regarding testing the motor, well you can just jam the wires onto a 1.5V AA cell and it should run.
Servos are easy.... have a look here
for that. But it's bad practice to give the servo its power from the Arduino- the red and black should come from their own source like a battery, and you need to connect the battery ground to Arduino ground.