On https://www.planetside2.com/home in the top right corner of the page click on "PC Version", then find "Already have a Daybreak Account? Download the Game." Click on "Download the game" chose a location to save the installer if needed, and wait for it to download.
So that's the problem. laucher not boot when you press a button to download. And my friend from the Ukraine can not register. I checked. I do not moguts zaregischtrirovat new account. Page registrpatsii darkens and becomes inaccessible. I am from Russia.
Or download it through steam, if you use it. But watch out: The client downloaded through steam is old, and you will need to do a huge load of updates.