I give you 2 solutions:
1 the official one: Add the driver to classpath, never mind where the applet and the connector are
it would be something like this:
JAVA_HOME=/usr/local/jdk1.x
export JAVA_HOME
CLASSPATH=${JAVA_HOME}/lib/tools.jar
CLASSPATH=${CLASSPATH}:${JAVA_HOME}/jre/lib/ext/theconnector.jar
export CLASSPATH
(is an example)
2. not official one (but it works!): unzip connector.jar, do it with winrar (
WinRAR archiver, a powerful tool to process RAR and ZIP files) when you unzip there are folders in a hierarchy order,
start with 'com' folder,explorer it: com->mysql->jdbc, copy 'com' folder (with its content) into directory where there are the applet whose connect to mysql
and that is!
good luck!