If I connect my Fire HD tablet micro USB socket to the HDMI input on my TV, will I see the output from the tablet on the TV, or is some additional software/hardware required?

I've seen adaptors to connect the two, but the description of their function isn't very clear.

The easiest way to do it is to buy an Amazon Fire Stick which plugs into your TV's USB socket. You can then cast from your Fire tablet to your TV wirelessly via the stick.

It's not the USB socket you use, it's the micro-HDMI socket (left hand one of the two) - and nothing else is required, it's just like plugging a BD Player in to your TV via HDMI.

Just something to note though, some apps dont allow you to send video to a TV, and some apps wont run at all if you have a HDMI connection on the device.

Sky go and Now tv are 2 that wont work on either of my android boxes, or my tablet.

Oops yes I made a mistake. The Fire Stick plugs into a standard HDMI socket on your TV for visuals. It can plugged into the TVs USB socket at the same time for power but it's best to use the mains. A mains plug with USB socket is provided.