There the metal sheet that needs to pushed out is normally showing a spherical elevation and a recessed or cut out area where to place the marker. Then simply push in ARROW direction. Pushing with the pusher slightly tilted to the back helps to apply more force.
The location marked in green at the opening (hole) where you place your pin pusher to push the metal sheet out that connects the links. The shapes vary from bracelet to bracelet. Even from the same manufacturer. The elevated nibs on the metal sheet hold it in place resting in the circular cut-outs of the folded bracelet sheet. To re-insert, simply push them against the arrow direction. Again the disposable plastic cigarette lighter makes in inexpensive pusher, or any PVC block you might have handy.