build 2 6x6 blocks of dence residential, and industrial. surround them with road so that they are next to each other.. like this (R=road, I=industrial, H=residential)
RRRRRRRRRRRRRRR
RHHHHHHRIIIIIIR
RHHHHHHRIIIIIIR
RHHHHHHRIIIIIIR
RHHHHHHRIIIIIIR
RHHHHHHRIIIIIIR
RHHHHHHRIIIIIIR
RRRRRRRRRRRRRRR
Then build a power station (if it's coal build it a little way away), and connect up the zones with power cables. You don't have to completely cover the zones but make sure the cables are connected up and running across.
This should start building up, keep doing this in 6x6 sections if you can. Otherwise remember zones won't get built on if they are unpowered or more than 3blocks away from a road or other transport (I think subway stations work aswell but you won't be building them for a while).
There's a little bar on the left which shows you how much things are in demand. You won't need that much commercial until later on, so I'd build a few blocks of light commercial here and there. You can always bulldoze it and dence it up later. The demand is also a good indicator of how much you can tax stuff. At the start I normally go for higher tax on residential than on Industrial and Commercial, Don't go too high though, and if the residential demand starts dropping loads then lower it.
Getting a bit advanced now, but that should start you off. Experiment, it's sort of the point.