The Haunted Carriage shoots from Ashworld Manor every Tuesday D2R Items and Saturday between 12 pm., 8:30 pm, and 10 pm (based on your local server time). It's usually recommended that you arrive at in the early hours to make sure that you don't miss the opportunity to shoot however, that's more of a general suggestion rather than a demand. In any event, as long as you're in the nearby vicinity of the carriage, you should get an on-screen prompt that informs you that the contest begins and asks you whether you'd like to take part.
After the Haunted Carriage is born, it will follow a pre-established route until it reaches its destination. You can just stop by the Haunted Carriage at any point along the traveling to its final destination (or simply stay in the area until the final stop) However, you're much better to track the vehicle as it travels along rather than only participating in a limited portion of the event. For your reference, here's a map of the route taken by the carriage across the area (map courtesy of Wowhead):Once you've tracked down the carriage, it's time to join in the fun the event itself.
The Haunted Carriage moves along its designated route it is occasionally threatened by guards. Guards' locations are indicated by skulls on the above map. There's a possibility of a variance in the location, precisely, they spawn, but you'll typically see them within the general area.
Guards aren't particularly tough (especially if you're participating in this tournament with other players, but they're a good source of gold and gear drops. It's the reason why it's recommended that you follow the carriage all the way around so that buy diablo II resurrected items you can participate in as many of those guard fights as possible.