The driver you have is a "step and direction" type where the direction pin is pulled low or high to determine the direction of rotation and the step pin (on yours it's called "pulse") is pulsed to rotate the motor. In addition you have an enable pin that is pulled high to basically turn the driver on.
You also have dip switches to set microstepping options. Looking at the data sheet you have 15 microstep options which is much more than usual.
A good tutorial can be found here: http://danthompsonsblog.blogspot.com/2008/09/easydriver-v31-tutorial.html
. It is for the Easydriver board but most of the tutorial and code is applicable to yours. The only confusing part may be that the Easydriver has a ground for both step and direction. In your case you would tie the separate grounds together. And yes, the driver grounds and the Arduino grounds should also be tied together.
The data sheet states the driver will deliver up to 4.5 A so unless you have a very large motor you should be OK.
It looks like the Wantai driver has a lot of good features. Let us know how it works out for you.