First, make sure you've set your computer to allow you to see hidden folders.
Next, launch the game, and get to the character selection screen. No need to log all the way in, just do this so that the game can create the new data paths.
Log out. Now, go to where the data USED to be. Remember, this only applies to people who logged in at some time since 1.88 went live:
Vista users: C:/Users/(your windows login name)/AppData/Roaming/Electronic Arts/Dark Age of Camelot
Everyone else: C:/Documents and Settings/(your windows login name)/Application Data/Electronic Arts/Dark Age of Camelot
Leave this old folder open for a minute. Now, go to the new folders. The chains are almost the same, but now, there is another bit at the end. The new bits are the names of the different clients:
/Dark Age of Camelot/LotM
If you are a Pendragon player, you've got an even longer new file path!
Dark Age of Camelot/Test/LotM
Select user.dat, (character).ini, and (character).ign files in the old folder, and copy them to the new folder.
Relaunch the game.