Is it possible to import a hosted TypePad blog into WordPress self-hosted, including all of the image files and other media? I generated an export file from within TypePad but it is just a text file with the image URLs contained within the post content.
The export file isn't supposed to contain actual images--just references to them.
When you do the import (as @Philip directed), it's important that the images still be available via http in those original locations. WordPress downloads them and adds them to the local media library during the import process.
We've also modified the WordPress importer to import files without extensions, which are exceptionally common, and then rename them with an extension once imported. Our process makes all the added steps in the answer provided by Sahas Katta unnecessary, though his solution is the best possible solution when dealing with the default process.
You can check out our service at: tp2wp.com
Yes, you can login to your WP site,
go to Tools => Import and from there you can select to import the TypePad file you have generate, it's a very simple process.
You got the first step down. Just get the post text imported and working.
The next step is to use a plugin that imports external media attachments. W3 Total Cache has an excellent feature for that in it. It will import all external attachments and add them to the WP Media Library. It also has a "Modify Attachment URLs" tool. This will scan through all the links in your post and rewrite them to properly reference the images it just imported.
Always keep backups. If it messes up something, it will be easy to go back.
There might be a better plugin out there to do this, but I happened to be using it for caching anyways. If you aren't caching, I'd recommended this plugin anyways!