On the console version, you can read the newspapers weekly events. The change every week and it's random on which event will happen on that week. On Sundays, the weeky events on the newspaper are updated.
And what Alexandria said:
"I don't usually read the Sim paper, but if you go to map view during the day there will often be the star to mark the opportunity. If you just go to the park while that star is there, you'll be given the opportunity."
Is still the same for the console EXCEPT it's not a star. The Community lots where these events are usually held will have a glowing circle around them (the outline of the button will glow). I haven't had a chance to participate in that event yet but I think you need at least 1 logic skill to activate that event when visiting the lot. I remember trying once and at the time I didn't have a logic skill and I waited on the lot till nightfall and it never appeared. So try it with a logic skill and see if it appears