I have developed an web application using HTML, Java Servlet and all. While developing I was using Tomcat to deploy it in order to test it.
Now my development is don
You will have to build a WAR of the project. You can do this
via ant using the war task
The ant option is better because when you have multiple developers on the project and the code is in version control, it is easier to get the project automatically (using ant) and build a war. (you have version control, don't you?)
But this is more of an operational difference (albeit an important one) but the war created in either way are same
Deploy the war to the server
You can manually copy the war file to the $TOMCAT_HOME/webapps directory (See the "Creating and Deploying a WAR File" section on this article)
You can use the Tomcat 6 "Manager" application.
Update
You said that you are using MySql also. MySql should be installed on a server (it can be on the same server) and the configuration should be changed (username, password, server details) so that the application connects to the same database (I am sure you are not hard coding database details and credentials in your application and reading them from some configuration, this is the configuration that has to be changed)