Replacing a thermal store - hot water cylinder?
Just opening the taps will not drain the cistern, as the supply piping only runs through a heat exchanger inside the unit.  Disconnect the power supply long enough ahead of time that the water cools down before attempting anything - per the manufacturer the water in the cistern will be around 55°C, which is hot enough to cause scalding.

With the exception of the cistern, disconnecting this will be similar to disconnecting a tankless hot water heater here in the States. Turn off the cold water supply first, then put something to catch water under the connection for the hot water outlet.  If there's a cut-off on the hot water side, close it.  If not, make sure all your taps are closed while you disconnect the hot water supply from the unit.  This will be kind of like holding your thumb over the top of a straw - it keeps gravity and atmospheric pressure from draining all of the pipes in a torrent as soon as you disconnect it.  After you have the pipe open, have someone go around and open taps one by one to allow the supply side to drain out while you catch the water.

I can't tell from the documentation I could find if there's a drain for the cistern or not, but I'd be surprised if there wasn't.  Look for one at the bottom of the unit (you can see the drain on the bottom of the new model you linked to).  If there isn't one, you may have to resort to sucking the water out through the cistern fill port with a wet-dry vac.