Mapbox launched Mapping with OpenStreetMap Mapping guides. The guides offer comprehensive training with JOSM including how to become a power mapper and validating OpenStreetMap.
We also found this JOSM Basic Manual pdf on the web, it would be good for a print out.
Additional JOSM tips:
Activate Remote Control. Make sure Remote Control is turned on (this allows the HOT Task Manager to send data directly to your JOSM session): go to Edit⇨Preferences; on the left click on the Remote Control icon (third from bottom), put a check in the box “Enable remote control”, click OK.