why are pm (permanent magnet) machines synchronous? and how do I start them?
it seems that this behaviour is due to the fact that two magnetic
  fields try to allign, with a torque that's proportional to the product
  between their magnitudes and the sin of the angle between them.


Magnets will try to align themselves for the strongest combined magnetic field. This phenomena is described by Lorentz Force and the Amperian loop model.

The 'sine' factor comes from having the magnet on a rotating shaft. When the magnet pole is aligned with the stator pole there is no rotational force because the field cannot get any stronger. Rotate the magnet in either direction and it will try to move back. However as it is going 'around the circle' the rotational force will decline towards zero as the rotor approaches 180&deg;, then increase again as it completes a 360&deg; revolution.   


  I also read that a pm machine will either run at the excitation field
  speed or not run at all. No idea why is that,


To understand why the motor must rotate at synchronous speed, imagine that the excitation frequency is zero (ie. a static stator field). The rotor will stay in one place (unless pulled away from it). Now slowly increase the frequency while allowing the rotor to be dragged around by the rotating stator field. 

So long as the rotor can keep up it will stay in sync, lagging slightly behind in phase (not frequency) due to torque loading and inertia while accelerating. But if it lags too far behind it will lose torque and snap around in the other direction. If it can't keep up then it won't run at a lower frequency, but simply jitter back and forth.


  how would I start them? as soon as I give them a rotating field, since
  they are not moving they have different velocities...


A synchronous PM motor will not start itself unless the starting frequency is low enough for the rotor to stay aligned to the rotating stator field. Since the rotor has inertia it must come into alignment and accelerate fast enough to keep up with the increasing drive frequency as it is brought up to speed. If it can manage to do that then it will be running at the same velocity (averaged over a cycle) lagging behind only in phase.


  and what if, by any chance, when I start the machine the two fields
  are aligned? 


If powered at mains frequency the rotor won't be able to accelerate fast enough to get up to speed in less than 1 cycle, so some other method of starting is required; eg. squirrel cage to create an induction drive, a separate motor to run it up to speed, or a spring that flicks the rotor in the correct direction when it starts going backwards (used in synchronous clock motors).

There is one other way to run a synchronous PM motor - electronic commutation. The rotor position is determined using Hall effect sensors or by reading back-emf off an unpowered stator coil, then the correct drive frequency and phase is synthesized by the motor controller. This operation is basically the same as for a Permanent Magnet Brushless DC (BLDC) motor.