The pusher is fixed/attached with a small circlip from inside the case. Should be a simple matter of opening the case up, uncasing the movement and refitting.
If you've never worked with handling watch movements or repairs before, I would suggest finding an experienced and competent watch repair shop or watchmaker to handle this task. Should be fairly simple, and if parts are missing, they should have something on hand that they can likely use (i.e. that circlip, which should be floating about somewhere inside your case still).