Here's how to:
1. First, be VERY aware that the design of the door and jamb means that it is sadly*** way too easy to damage the front lower corner of the door if the door opens too far. Rig up something to prevent your door from opening too far as you work on it.
2. Open the door to its normal full-open position, keeping #1 in mind.
3. If your new door check has a bend at the closed end, orient the check so that the bend points outward (away from the car). With the style of door check you have, this means that the check will be "right side up" on one side of the car and "up side down" on the other side of the car.
4. Locate the white roller in the middle hump of the metal spring. Yes, it would be easier to squeeze the open ends of the spring together if you kept it at the end, but IIRC the assembly is too long to fit between the door and the jamb if you first mount the spring to the loops on the jamb and then try to swing the spring over and fit it into the door.
5. I have used channel-locks as you pictured to squeeze the spring so its nipples fit into the door jamb loops. But I wonder if using a suitably sized Ideal-style worm drive hose clamp would be better...less hand strength required plus I would expect less chance of scratching the paint on the jamb and the spring.
6. Put a dab of heavy grease on the jamb loops. I don't think there is a need to lube the white roller or its axle. Fit the closed end of the spring into the hole in the door, compress the open end of the spring and line up the nipples on the spring with the loops, and put into place.
7. Now fit and fix the base plate of the check to the door with the two 10mm capscrews.
8. CAREFULLY and SLOWLY swing the door from open to closed position, being ready to stop in an instant if any metal to metal contact is heard. This step is mostly for the benefit of those doing this task using parts from sources other than our trusted vendors that may look similar to the X1/9 part but might have a different curve intended to fit another car.
Hope that my memory is accurate and that the above steps help!
***NEVER
ask me how I know this!!