There is quite a way to go, however. Before the SpaceX will be allowed to carry astronauts it has to show to the world that it is reliable when it comes to taking up robotic spacecraft. Even though today’s launch was successful, that is still some way away.
Once that happens, with the Dragon Spacecraft atop, SpaceX's Falcon 9 should be the first private sector space operator. Below is the design of both Falcon 9 and Dragon. It is hoped that in the future the Dragon section will be filled with supplies for the International Space Station and then, after that, visiting astronauts. We cannot seem to find out how much SpaceX will charge for each astronaut, however.
Perhaps they will give NASA a discount for the heavy investment in the company?