I bought a copy of MagPi, and my Raspberry Pi Zero does not light up when I apply power. But if I connect it to my PC with a USB cable the Broadcom BCM2708 Boot device is detected, so I assume it is working. I haven't tested with SDcard present.
Yes I also did connect to my linux laptop and it also detects the Broadcom BCM2708.
I was expecting to be able to connect it to a linux box via usb as it is and open a ssh connection through tty but they didn't made it that easy it's a shame.
On a normal Pi the red light comes on when there is 5v and the green light flashes during disk activity like booting, I would bet the zero is similar. Don't use a cheap phone charger, use a good quality 1-2 amp power supply. Also be sure your sd card was correctly burned. Use the instructions and tools from raspberrypi.org--there are lots of crap SD burning tools so avoid them all. Try a different sd card and again use a good brand.
Someone have a different experience or can tell something about this ?