Q:

Eclipse not detecting the installed java

I had installed Eclipse Galileo first and after that installed Java.
But it is not detecting my java.
What configuration changes can I make so that Eclipse can run my java programs?
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A:

You can specify the exact jvm you want to use through:

a -vm argument
directly within the eclipse.ini

Once started, you can reference as many JVM you need in the Installed JRE preference panel
alt text http://img168.imageshack.us/img168/3307/eclipseinstalledjre2.png
Finally, you need to reference the JVM you need in the Libraries tab, in your Java Build Path properties of your Java project (as mentioned by Steve in his answer):
alt text http://img52.imageshack.us/img52/5947/eclipseinstalledjre3.png

A:

It seems, that your project doesn't have the JVM in it's Build Path. 
Right-Click on your project. Choose Build Path --> Add Libraries.... Take JRE System Library and choose a JVM for your project.

