Commonly referred to as Old German Script, Kurrent is the most common handwriting style in use in Germany from about the mid-16th century into the early 20th century, and will be found in handwritten documents, letters, and record book entries. The blackface type known as Fraktur was used to print many of the old German books, newspapers and documents. For more recent, 20th century records, you'll also want to become familiar with the Sütterlin script.
For documents written in the old German script, the Kurrent Kupferstich font created by Walden Font Company is an excellent learning tool. You can type in a word or phrase from your document (in German, of course) as you think it should read and then convert it to the Old German Script with this font to see if they match up. While there, explore the many other historic fonts they offer. They are beautiful and historically accurate, perfect for family history books, scrapbooks, or other printed projects.