How would I make an HTML-based application from existing Java code

How would I make an HTML-based application from existing Java code

I'm trying to make a web-based application that can retrieve, modify,
delete data, and add data to a relational database. I've created a simple
database and written up some Java code that can perform all of these
actions with the database.
However, one of the stipulations for the creation of this application is
that it must be HTML-based and cannot use Java applets, Flash,
Silverlight, or other plugins. Does that mean that I'll need to scrap all
of my code (along with all of my work), or is there some way that I can
adapt my code to fit within this constraint? Also, how would I go about
making this into a web app?