You make a character and try to get to 60 without dying. Pretty straightforward. The game is the same as non hardcore to play, except dungeons can only be done once a day each until you get to 60. You are allowed to group, trade, use mail and auction house. Join a guild if you like to socialize.
They’re doing an optional SF (self found) mode sometime soon I hear. You will not be able to mail, trade or use auction house. You are able to group though.
If you die you either delete, or you can transfer to the Era servers and continue with your character.
This thread has some good tips for a success run,
Best of luck!