Richard Branson claimed that his Virgin Galactic would bring tourists into space within a period of 19 months. Today, this has not happened yet. However, it will happen in the near future! The technology is there, it just needs to be used in the right way.
Buying tickets: tickets will be bought from spacelines, something similar than airline ticket sales. Funny enough, you can already apply to fly with the Virgin Galactic at this very moment! Once accepted, this will only cost you $250,000.
What about security? Passenger checks will be required, very similar than in airports.
Travel insurance? Sure, however for this type of travel you could be looking at something between $10,000 and $30,000.
Are you interested in going to space, then you should read more about it right here