Anyone who has seen handwritten German sources from the nineteenth and early twentieth centuries will know that the handwriting at the time was very different from what they know today. One way to learn this script is with a so-called Deutsche Fibel, a German schoolbook designed to teach kids reading and writing. To help those who are new to this script, I have scanned and uploaded such a schoolbook to Google Docs.
In order to learn how to read the script, you might want to learn how to write it, at least in the beginning. The letters will be easier to remember that way.
Update (8/18/2010): Someone has gone ahead and uploaded the scan to the Internet Archive. If you would prefer to use their interface instead of Google Docs, here: http://www.archive.org/details/DeutscheFibel. That will be especially handy if you don’t have a Google account.
Update (2/28/2012): I just realized that the Internet Archive links back here for the PDF version; however, you can still get around Google Docs with this direct link to the PDF on the Internet Archive. Sorry. Next time I scan something, I will simply throw it up on the Internet Archive directly, now that I know how it works.