The Youtube video that mnorian posted is a great start as far as setting up the kind of motors you'd find in consumer electrics (washing machines, vacuums etc) but even then some of those motors are more difficult to wire (or impossible without the proper controller).
There are any number of different motor for different applications. There are AC and DC motors, synchronous and asynchronous motors, single and multi phased motors, stepper motors and servo motors just to name the kinds I can think of off the top of my head. It's been 50 something years since I looked at the electronic design and operation of the basic motors so probably a lot has changed since then (e.g. the introduction of stepper motors and the use of servo motors).
Obviously wiring a DC motor is going to be the easiest (generally) because you basically just put your battery or DC supply across it and it should run, forward or backward, depending upon whether or not there is circuitry to limit polarity. A basic single phase, capacitor start, AC motor could be the next easiest to wire... provided the capacity is present and in good condition. An AC voltage (active and neutral) across the contacts is probably likely to kick it into action (note the double uncertainty... Murphy's law is always present). After that... it starts to get a bit more involved. You may need to check the web for specific motors.
