As was mentioned, your V5 characters must be adults for 48 unpaused hours before you can use the dating show.
When you activate the dating show, a SELECT? message will appear. Scroll through your V5 adult characters and pick which one you want to mate.
The matchmaker will appear on TV and show a prospective mate to you. Select MARRY! or CANCEL.
As was mentioned, you can view the dating show three times each day, at any time of the day (as long as they're awake.)
If you select MARRY! your V5 adult that you picked will say goodbye to their siblings (and parents if you're on generation 2 or higher). The siblings (and parents) will leave. Now the mate from the show will show up on your V5. They will kiss, and transform into parent characters. Then 1 to 3 eggs will appear.