Cleaning
Because the bio-ethanol fuel burns so clean, there is minimal residue present on the burners or media within the unit. They are much smaller, and require less upkeep, but they still need occasional attention. Using a gas fireplace glass cleaner on the surrounding protective shield works well and using a damp towel to wipe the surface of the unit will get all the usual house dust that may accumulate. Of course,all of this is done while the tabletop fireplace is not in use, the fire not lit.
Storage
The most important thing to remember is to dump the fuel, or let it burn off completely. Storing anything with an internal accelerant is dangerous, as gases can build up, only needing a small spark to ignite. Let the fuel within burn or dump it into a safe receptacle, then, if you still have the box it came in, store it in its original container.
If it was purchased without a box, select the right size at a home improvement store or shipping company, and add some bating to the free space within to keep it from shifting while stored. Place in an out-of-the-way space like a closet or an attic.