Required hardware:
The board itself (Zedboard, ZyBo, MicroZed or SocKit)
A monitor capable of displaying VESA-compliant 1024x768 @ 60Hz with an analog VGA input (i.e. virtually any PC monitor).
An analog VGA cable for the monitor
A USB keyboard
A USB mouse
A USB hub recognized by Linux 3.12.0, if the keyboard and mouse are not combined in a single USB plug
For Zedboard and SocKit: A type A USB receptacle (female) to USB Micro B plug cable (included in Zedboard's kit, but doesn't arrive with the SocKit)
For Zedboard: A reliable SD card with 4GB or more, preferably Sandisk (the one that came with the board should not be used).
For ZyBo, MicroZed and SocKit: A reliable MicroSD card with 4GB or more, preferably Sandisk.
Recommended: A USB adapter between an SD/MicroSD card and PC, for writing the image and boot file to the card.