1. If you ask how DOES it work - simply put - the device (PS3, 3D BD player etc.) generates two pictures - one for each eye and the TV or display must asure that correct picture is delivered to the corresponding eye.
2. 3D TVs are clearly marked / marketed / 3D functionality is listed in their specs. Basically any 3D TV on the market like from Sony, Samsung or Panasonic should be compatible. There are some small nuances like maximal frequencies or type / version of HDMI connection etc. but I doubt there is any 3D TV currently available not compatible with let's say PS3.
3. Corresponding firmware 3.30 (I believe) for 3D Games and 3.50 for 3D movies. 3D TV - obviously - connected by "3D" HDMI lead (basically one capable of v1.4 HDMI frequecies) and indeed 3D active / shutter glasses.
4. Yes you do - all current systems use active 3D shutter glasses.