This article was written for Thunderbird but also applies to Mozilla Suite / SeaMonkey (though some menu sequences may differ). This article gives step by step instructions for how to import folders from another profile for a new user who has never installed an extension. It assumes you're using Windows but you should still be able to follow the instructions using a file manager on another operating system. The ImportExportTools extension can also be used to export folders.
Install the ImportExportTools extension
If you can't download the add-on the problem might be due to a optional download manager. One way that could occur is if it changed the file extension from .xpi to something else. However, it is also possible to find and install the add-on from within Thunderbird. The reason why its a fallback plan is the "search for add-ons" feature in Thunderbird doesn't find many add-ons. However, it does find this one.
Find your old profile
Your folders are stored as mbox files in a profile. These are text files with the folders name and no file extension. For example your inbox folder is the "inbox." file and the Sent folder is the "Sent." file. You can safely read one using a text editor to verify it contains mail messages though its not user friendly because it contains the raw message source, including all of the headers and big blocks of characters all run together whenever you have a binary attachment.
If you're running Windows 2000 or later you may need to enable "Show hidden files and folders" and disable "Hide extensions for known file types" (its under the Hidden files and folders heading) and "Hide protected operating system files (Recommended)" in Tools -> Folder Options -> View to see it. You may get a warning message that your computer won't work if you do this. Changing those settings causes no harm, its really warning you not to change or delete any of the files or directories used to store the operating system. See this thread if you're running a older version of Windows.
Find the mail folders
If the folder was in Local Folders or you used a global inbox it will be somewhere in the Mail\Local Folders directory within the profile. Otherwise look for a subdirectory named after the accounts mail server. For example, if you're using a Gmail POP account your inbox folder would normally be the "inbox." mbox file at Mail\pop.gmail.com. If you have multiple accounts with the same email provider the subdirectory might have a numeric suffix, for example Mail\pop.gmail-2.com.
Ignore the .msf files, they don't have any messages. You want the files with the folders name and no file extension.
Thunderbird uses *.sbd subdirectories to create a folder hierarchy. So a Local Folders\1\2\xyz folder would be stored as a "xyz." mbox file at Mail\Local Folders\1.sbd\2.sbd\3.sbd . That directory would also have a empty xyz.sbd subdirectory created in preparation for you someday creating a child folder of xyz. Ignore it.
If you have "Allow Windows Search to search messages" checked in the options you will see *.wdseml files. If you are using OS X and enabled Spotlight Integration you will see *.mozeml files. Each file is a partial copy (up to about 49KB) of a message in the mail folder, stored in a .mozmsgs subdirectory. Ignore them. You only want the files named after the mail folder with no file extension such as "inbox.", "sent." etc. Ignore them.
Import the folders
Your folders are stored as mbox files in a profile. These are text files with the folders name and no file extension. For example your inbox folder is the "inbox." file. DO NOT try to import "inbox.msf" or "inbox.sbd" - the messages are in "inbox.". That naming convention causes a lot of confusion, it would have been a lot easier if the mbox files had a .mbx or .mbox file extension like some other email clients use.
The previous sections explained how to import mail folders stored as mbox files. That is the default way to store mail in Thunderbird.
Tools -> ImportExportTools -> Import Messages and "Import all messages from a directory" import .eml files. That is mainly used to import messages from other email clients that don't support mbox files such as Windows Live Mail. Thunderbird does support configuring an account to use maildir rather than mbox to store messages. Thunderbird's implementation of maildir stores all of the messages as individual files using the .eml format. Each file has a filename that is a string of digits and has no filename. Because they don't have a .eml file extension you need to choose "All files" in the file picker.
One user reported that they if they didn't limit the number of directories of *.eml files to import in one step to about 30 it always created the corresponding folder, but some would have no messages. 
Export the Folders
You could export your mail folders instead as mbox files using using Tools -> ImportExportTools -> Export folder, as *.eml files using Tools -> ImportExportTools -> Export all messages in the folder -> EML format (you could import them later on using Tools -> ImportExportTools -> Import All Messages from a directory -> also from its subdirectories), or in several different formats that are only meant to display the contents (can't import them).
Don't worry if you don't see exactly what is in the screen shots above. The menus for the ImportExportTools add-on have changed several times. The Tools menu might change in future versions of Thunderbird. Its screen shot has four entries from other add-ons.