Ant is a build tool. Although IntelliJ does that for you, you need IntelliJ to do this which means you can't distribute your application without IntelliJ.
Ant uses a dependency matrix for building. This is sometimes difficult for developers to understand, but it basically means that you define the steps, how the steps are dependent upon each other, and let the build tool figure out exactly how to do its job. Ant is for Java like Make is to C and C++ applications.
Ant uses targets which are the steps you specify to do. For example, you might have a target called package that will build your jar or war. That target might depend upon another target called compile to compile the code. That target might depend upon a code generation phases (like if you had WSDL files).
Each target is a set of tasks. For example, the compile target is likely to have the <javac> task in it. It might also need the <mkdir> task to create the work directories where you classfiles are stored.
There are plenty of books on Ant, and there's a tutorial on the Ant Website. You didn't explain the issues you were having, so it's hard to be more specific than this.
Ant can also run your unit tests too. There's a <junit> target which can run the tests, and you specify whether or not you want to run almost all of your <junit> tests via the <batchtest> sub-entity or if you have a program driver you specify via the <test> entity.
Once you get an Ant script that can build and run your tests outside of IntelliJ, you can now get a Continuous Integration tool like Jenkins. A continuous integration tool watches your repository for changes, and if a change occurs, will then build your application. It's a great way to catch errors early on.
What does this have to do with Continuous Testing? Well, if you have your Ant script able to run unit tests, the Continuous Integration engine not only can build your app, but then run the unit tests with each and every change that occurs.
Jenkins is nice because it's very simple to use. You download a jenkins.war and you can launch the Jenkins webpage via the java -jar jenkins.war command. This brings up a web server on port 8080 on your machine. Obviously, Jenkins can be configured to run on different ports and under Tomcat if you so desire. It can integrate with Windows Active Directory, LDAP, and many other user verification systems.
Jenkins will show you charts and graphs of your tests, let you know which tests failed or passed, and will notify you of any problems via email, tweets, IM, Jabber, and even Facebook posts. People have even setup a traffic light in their offices that turns red when builds or tests fail.
Take it one step at a time. Get a good book on Ant. Read the tutorial on the Ant website. Then try to get a working Ant script to just to build your app. If you are having specific issues, you can ask for help.
Once you have the build going, extend the script to run your unit tests. Once that is done, download Jenkins and try to get that up and running.
