How do I extract source code from a Jar file?

A jar is analogous to a zip file, so they may or may not contain the source code you need for development. You can read about jar files here.

I've received source code for a Java product ...

If you have really received the source code of a product, and all you've got is JAR files, then the JAR files (which are actually ZIP files with a different file suffix and a particular kind of "manifest") should contain a bunch of files with the file suffix ".java". You should be able to check this using any ZIP archive tool.

If there are no ".java" files in the JARs (e.g. only a lot of ".class" and other files), you do not have the source code for the product. Making changes will be really really hard, given that you are not a Java developer.

Assuming that you are doing this legitimately (i.e. with the explicit or implicit permission of the product's developer) you will save yourself a lot of time if you can also get hold of the product's build instructions. For example, if it is built using Ant, you want the "build.xml" file(s).