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 us

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.