How do I access/manipulate that database from my Java application? The instructions for my project suggest using NetBeans, but I'm not keen on installing an IDE just for one project if there's another way (I'd also like to learn the right way.... I'm sure not everyone who uses databases with Java installs NetBeans...).
If someone could point out where to start......
When you do things right, people won't be sure you've done anything at all.
Nope, you don't need NetBeans -- not even sure why someone would suggest that. You need to use the JDBC API, which is part of the standard JDK; it's the java.sql package. The API is the same for every database, but you need a "driver" -- a special JAR file -- for whatever database product you're using.
You can get the MySQL JDBC driver here. Here is the Java Tutorials section on JDBC, which is a decent introduction.