Start with the power station. I use the coal fired power plant because unlike those worthless greenie inventions (I kid!) you can build on top of them. They are heavy as, so stick them in the very centre.
As no-one wants to live near a power plant, I surround them with office blocks.
Next I put an elevator tower so that both the office blocks and the residential blocks can turn into high-rises. And outside that I start with the residential blocks.

Your city will need the police, fire department and hospital or it will start to fall apart after too long. I usually start by placing the train station on one side.
Then I put the police station on the other side. The hospital and fire department can then sit on top of the train station.
You might also like to put your first unique building on top of the police station, but only if it is not too big and heavy. The mansion from free-play is just fine here. You might also consider putting your army barracks here too.

Now build your office and residential complexes up to their full 2x6 height. If the conditions are right, they will automatically turn into high-rises.
If you are having trouble turning the residential blocks into high-rises, remember to place plenty of trees around. You can also put a terrace and add some more trees on top.

Now we need to prepare for the next level of our city.
Add a single layer of housing blocks to the residential high-rise. This should bring it approximately level with the office blocks.
You can place whatever you want on top of the power stations, providing they aren't taller than an office block.

Now place a single street block in the middle, and two street sections on each side. Don't overlap them or the street sections wont be level.
Now you can get started on the second level, placing the power stations, office blocks, residential blocks and elevator shafts just as before. You shouldn't need to add any more police stations, hospitals, army barracks or fire stations. Although it's a good idea to keep placing missile turrets wherever you have space.
Enjoy.

Keep building each level in the same way. Always try to get your residences and business blocks to combine into skyscrapers whenever possible.
You may need to modify the design somewhat to accommodate the unique (star) buildings into your city. You may need to place the larger ones in the center line of the city as they can be heavy.
Remember the key to keeping your city from falling apart is that the weight of buildings above press down on the buildings below and keep them together.
See how the business towers sit on the ends of two of the road sections. This keeps everything together.

Don't forget to turn on disasters for extra fun. This will really test your city!

Uh, oh.