Where the activity shows up, that's up to Facebook by default. All activity is entered into the users Activity Log, which is part of the user's Timeline. The default activity action is to "Let Facebook choose to show it". That will then push the event to the user's profile feed, their friends feed, and/or the ticker depending on social relevance of that action to the viewer. If the action, site, or app is popular among a group of friends, it's more likely to appear to those friends when any of them take that action.
You can click the white-circle next to the action to change the behavior of that action for your own news feed to either show it, don't show it, or let Facebook decide (the default).
Hope that explains,
Alex