Begin on the driver's side of your 525xi. The wiper is held in place in the back by two small wings and in the front by a tab. Push the front of the wiper down so the tab pops out of the slot. Note: if you have OEM blades on your car, they will release in reverse -- push down on the rear of the blade so the wings disengage.
Attach the adapter
Place the adapter on top of the blade. Line up the 'v' on the adapter with the 'v' on the blade and snap it in to place.
Position the new blade
Align the wings on the back of the wiper arm with the corresponding tabs on the adapter. Note: this is the opposite of how OEM blades come off the car and is counterintuitive.
Lock the blade into place
Push the wiper up towards the tab, which will pop into the slot. You will hear a click as it snaps into place.
You're all finished with the driver's side. Repeat the process on the passenger side of your 525xi.