The Haunted Carriage can be found in Ashworld Manor every Tuesday and Saturday between 12 pm., 8:30 pm, and 10 at 10 (based on your local server time). It is generally recommended that you arrive at the manor D2R Items within a minimum of 10 minutes prior to the scheduled time to make sure that you don't miss out on your chance, but that's more of a general recommendation as opposed to a formal obligation. Whatever the case, as long as you're in the nearby vicinity of the carriage, you should be greeted by an on-screen message that informs you the event begins and asks you for your permission to participate.
After the Haunted Carriage is born, it will follow a set route towards its ultimate destination. There is a possibility to simply meet the Haunted Carriage once it's on traveling to its final destination (or just sit and wait until the end of the road) However, you're better off following the carriage as it rolls along rather than just taking part at a part of the fun. For your reference, here's a diagram of the carriage's route across the region (map from Wowhead):Once you've located the carriage, you're now able to be a part of the event that is the event.
As the Haunted Carriage travels along its established route It is sometimes assaulted by security guards. Those guards' locations are shown by skulls on the map above. There's probably a tiny difference in where exactly the guards spawn, however, you'll typically see them in the same general region.
Guards aren't very tough (especially when you're taking part in this event along with other players), but they're a good source for gold and drops. It's for this reason that it's suggested that cheap d2r items you follow the carriage across its entire course in order to participate in as many of those guard fights as you can.