2- hold control and then click where you want to go. Note that you need to press control before initiating movement at all (in case you use the arrow path markers/2 clicks movement confirmation). I have had mixed success with this, often ending with less TUs than I thought.
IIRC, the "strafe" movement adds 1TU for "forwardish" or "sidish" movement, and 2TU for "backwardish" movement. Thus if you move to the right, that is normally a 4TU move that would leave you looking right, but it is a 5TU strafe that leaves you looking forward. A backwards-right strafe would be 6TU move that leaves you looking forward.
The strafe code only works to adjacent squares,. Thus you can strafe only one square at a time, you can't lay in a strafing path with one click. It is most useful for moving sideways into a corridor.
You can "strafe" tanks, but the vehicle turns its turret not its hull. The turret stays turned which is great for flanking attacks. IIRC it costs 1TU for up to 90 deg turret turn, which is cheaper than turning the vehicle.
Strafing movement is aware of terrain cost, and the TU penalty is in addition to that. There is no terrain cost for turning a turret.