First you need to have your event in the Open stage. To do this go to Manage events and select the event in question. If your event is in Pending stage progress it to the net stage by clicking the Progress to next stage button. This will move the event into Open stage which will ensure that users can sign up to it in their My events page. Only eligible players will see it.
There are other ways by which you can make the community aware of the event and you should contact the club's Communications manager to discuss what can be done. For example, an email could be sent out to members or a notice banner could be set in ManageMyMatch.
Importantly, ManageMyMatch provides a special URL that, when navigated to, will automatically sign someone up to the event. Click on the Details tab in Manage events and you'll see an "auto sign-up link". Copy that and use that in an email (or in the ManageMyMatch notice banner) to make it extra easy for people to sign up.