If the josm.jar file you downloaded does not open go ahead and create a text file named start_JOSM.bat in notepad the wite down the following: java -jar josm.jar. Now save this .bat file in the exact same directory where josm.jar is located. Next go and double click on the.bat file and JOSM will start up.
Notice I did not put quotes around any commands. The reason for this is to prevent confusion as in many software manuals a good practice is not put in any punction near verbatum commands to eliminate “polluting” your script.