You can travel to El Gouna from Cairo by bus. Bus schedule offers multiple daily transfer from Cairo at fixed times.
Bus schedule can be checked at the internet under:
You can also reach El Gouna from Hurghada International Airport which is located 30 kilometers far from El Gouna by taxi or bus.
You can also reach El Gouna by flights from Cairo to Hurghada. For schedule, prices, etc please check Egypt Air.
The nearest airport to El Gouna is Hurghada Airport almost 30 km from El Gouna. There are many airlines which offer direct flights to Hurghada from international metropoles at reasonable prices. Many tourist companies have good offers including accommodation.
Non Egyptians have to obtain visa to be able to enter the country. You can obtain visa at any international airport in Egypt. You have to go first to any of the banks at the arrival airport and by a stamp for US$ 20- and then proceed to the passport control.