The "Hall of Fame" lists the top players in various categories. Unlike the leaderboards, the "Hall of Fame" lists all-time records. This means that if you make it into the "Hall of Fame" and then leave the Ladder your Ladder name will stay in the Hall of Fame as long as your record still stands.
You don't have to do anything special to get into the Hall of Fame because it is completely automated. Once you have broken the record of the lowest listing in a particular category, you will be placed in the "Hall of Fame" within 24 hours.
There are many categories in which you may become listed. You can be listed in more than one category at once.
If you leave the Ladder or are deleted for inactivity while you are listed in the "Hall of Fame," your record will remain until it is broken by another player. Howeever, you cannot rejoin the Ladder and continue to build your original record.