You use the symbol Nameless posted and add the name of the player you wish to whisper (or PM as we call it). Once you did it once the whispered person will stay by default besides the " symbol. If you whisper multiple names you do " and then arrow down or up to switch between the various people you contacted or just arrow down till you have a clean " only and can add a whisper person to the list in use.
Mind you the names go away once you log out. ;)
Hope that helps
PS: One hint though, If you are planning on having a long conversation with a person I suggest to either invite that person in Party channel (by doing /invite NAME HERE) or by adding the person to your friendslist if you intend in keeping contact (/friendinvite NAME HERE). Why do I suggest this? Because when you chat too much in whisper (or in general chat for that matter) you get chat banned for spamming ;)
you can actually get chat banned for gen and wis chat?
As Nameless said it's a temporary ban. But if you get the temporary one minute ban and still continue to spamm the chat or whisper in general channel or trade channel it will increase to much higher durations. Hence why I suggested to either friendinvite the player or to create a temporary party for usage of the party channel :)