OmegaT.jnlpis downloaded, a double-click should open it in Java Web Start.app.
If that is not the case, if it opens as a text file for example, it means that .jnlp files associations to Java Web Start.app are broken.
To fix that, right-click on the .jnlp file, Choose "Open With", select "Others..." at the bottom of the list and browse your disk to find the application.
Java Web Start.app is located in
/Applications/Utilities/Java/for older versions of Java and in
/System/Library/CoreServices/for the most recent version of Java (Java update 4, released on June 15 2009).
Once you have selected the application, check the "Always open with" box at the bottom of the dialog.
Thanks to Yves who send me the comment that triggered this "investigation" and to this blog article that clarified everything.