Orion's first flight, EM-1, or Exploration Mission-1, is scheduled for June 2020. It's planned as an uncrewed test that will send the capsule around the Moon for six days, with a total mission duration of around three weeks. It was also supposed to be the debut of SLS, the Space Launch System, NASA's heavy lift rocket.
However, SLS has endured countless cost overruns and production delays, which has continually pushed EM-1's launch date further and further back. It seems as though this presidential administration is eager to have some forward progress on NASA's Moon program by 2020, so sending the mission up on a commercial rocket is the next best option. A decision on whether to move forward with a commercial operator will be made in the next few weeks.
There are only two heavy lift rockets currently in operation that are capable of supporting this mission, ULA's Delta IV Heavy and SpaceX's Falcon Heavy. It will take two launches to put the entire apparatus in orbit — one to launch the Orion capsule into low Earth orbit and the other for the upper stage of the rocket that would propel Orion to the Moon and back. This would be nothing new for NASA; after all, the organization has been doing orbital rendezvous and docking since the days of the Gemini program.
The real key here is that NASA has admitted that commercial rockets may be able to sub in for SLS. Yes, they might need additional rockets to do the job one SLS flight could do, but that isn't necessarily a bad thing. Construction in space is much easier and less expensive than launching one behemoth rocket. The question now is what does the future of SLS look like if NASA is starting to look at commercial options for its crewed missions outside of Earth orbit? It certainly will be interesting to keep an eye on this.