Dueling and Racing coasters are easy to build. To make a dueling coaster, both stations must be right next to other. The direction doesn't matter, but they must be both next to each other. Both coasters must also have the "Synchronize with adjacent station" option enabled. Examples of rides like this are Dueling Dragons at Universal Studios Islands of Adventure, and Gwazi at Busch Gardens Tampa Bay. The screenshot above shows an RCT version of Dueling Dragons

For "single track" racing/dueling coasters, such as the wild mouse in Diamond Heights, one side must be built, but for the final part of the track, it should finish one square off from the station, and then start a new station (station platform on the special menu) and then the other side of the ride is built, which will connect up to the first station. A real life example of this is the Racer at Kennywood or the Grand National at Blackpool Pleasure Beach..

Another type of Dueling/Racing coaster can be done by building the stations side by side, but in opposite directions, so on train goes out one side, and another goes out the other side. This works in standard RCT, but has problems in Corkscrew Follies