ArcGIS headaches

I’m trying to get GIS data that my city supplies into a usable format but I’m drawing a blank
It comes from ArcGIS, supposedly there is an exporting tool for this software package, but I cannot figure this out for the life of me.
Does anyone know how to take the data and turn it into something I can use in JOSM, and more importantly, will someone that does have that knowledge please share it with me>

What would you like to do with this data once it is in JOSM? If you plan to upload some of the data to OSM, then you first need to read these pages:

In particular, join the imports@ mailing list and announce what you plan to import and wait for feedback before uploading any data.

From looking at the site, the only layers which seem of use in OSM are the city limits, streets, and wetlands (and possibly landuse). For conversion from Shapefile to OSM.XML, I recommend ogr2osm, which is what I used to convert my county’s streets and parks:

More possibilities can be found here:

But again, please keep in communication with the community before doing any imports, as those with more experience can offer advice on how to properly convert the files.