Windows live mail uses a very different method to Thunderbird to store emails. In Thunderbird a single file is used to store all mail in a single folder. In windows live mail mail is stored as individual EML files in the mail folders.
There is at this point no direct import for those wishing to move from Live mail to Thunderbird. It is however possible.
Getting it all together
1. Install Thunderbird and the import/Export tools extension. Installing an extension is discussed here
2. Create your accounts in Thunderbird.
In windows live mail, starting with the Tools menu select Options then the advanced tab followed by the maintenance button Finally select the store folder button. This will show you exactly where Live Mail keeps your mail.
Use the import export tools entry on the Tools menu in Thunderbird and select the import all EML files from a directory, then the an it's sub directories menu option. Navigate the file picker to the location shown by Windows Live Mail and let it do it's thing. Now all of your mail and folders should be imported to Thunderbird under the Local folders in your folder tree.
Export your contacts from Live as a CSV file and import that into Thunderbird using Import on the Tools menu. Just be sure to click on the addressbook in the next window. Everything will not work.
If you are migrating from Live with Hotmail, ensure the account you create is IMAP or your folders will not import. If you create a POP account the contents of the inbox only will be downloaded to Thunderbird.