I shall assume you are simply talking about mafia's settings.
If you are a Windows user, then you probably saved the mafia .jar (or .exe) in a folder/directory. This is the ONLY directory that is used. Mafia, when first started, will have produced a load of sub-directories that it uses to store a load of stuff so you don't need to request it too often from the KoL servers. These will have names such as "buffs", "ccs", "clan", "data", "images", "relay", "scripts", "sessions" and "settings" (maybe not all of those, maybe some others) with stuff inside. To transfer all your settings and cached data, copy all of those across along with the .jar. However, the only really crucial one you will need is "settings" (and perhaps "data" if you use scripts from this site).
Mac users have theirs saved under "~/Library/Application Support/KoLmafia/". Take a look there and copy anything relevant across.
Linux users are a little more complex, but not much. Your files are all saved within a hidden directory under your account's home. Go to the account's home directory, and look for ".kolmafia". This is the directory to copy (same as in Windows) but must be saved in the account's home. So, if your username is grotfang, save it under "/home/grotfang/.kolmafia".
In short, counter values, password details and all that stuff is saved in your settings folder. Where you find this changes depending on your system.
EDIT: Given this question seems to come up in one way or another every few weeks, is it worth stickying an answer?