How can an applet talk directly with EJB?
This means that the J2EE and/or JNDI and/or RMI classes need to be present in the applet's Java Virtual Machine. The easiest way to assure this is to use the latest Java Plug-in. Netscape 6, aka Mozilla, ships with the Java Plug-in. Other browsers have various problems with RMI and JNDI classes that are beyond the scope of this answer.
Note, however, that it is not recommended to use EJB directly from applets, in part due to compatibility issues. Instead, you can use Servlets inside the application server to provide an HTML front-end that is assured to work on a much larger base of clients.