You have 2 problems. First, all the popular web browsers are equipped with really antique JDK's (pre-jdbc). That can be solved by using the
Java plug-in.
However, then you will immediately be hit with the next obstacle.
JDBC is considered "dangerous", so the sandbox forbids applets running in web browsers to use it (the AppletViewer IS allowed to use it). This could be solved, but then you hit the third problem.
Many DBMS's use private tcp/ip ports in their jdbc drivers - for example, SQL server uses 1033, PostgreSQL uses 5432, etc. So if there's reasonably tight firewall between the DBMS and the user, even a signed applet won't work.
Yes, it's a vast conspiracy. The whole setup is designed to (ahem) "encourage" you to use a 3-tier system, where the webserver does the actual talking to the DBMS. Then, on top of that, you'll discover that MS-Access is a stepchild DBMS in the web world - the jdbc-odbc bridge isn't threadsafe. For a major-league app you need a major-league DBMS like SQL Server, DB/2, Oracle - or - if you're cheap, like me - MySQL or PostgreSQL.