The roads are essential in keeping your city operational. They allow the citizens to travel around the city safely. They're also required for buildings to function and allow you to build Steam Hubs - smaller sources of heat that allow you to provide heat to buildings that are located away from the main Generator. This is why you need to invest in roads from the very beginning.
The roads have to be built in a certain way. They can either go around the generator, or be perpendicular to it. That's meant to save space.
If you want to build a road, go to the building menu and click the icon marked with a '1' on the screen below. This will allow you to build roads. You will be able to build a road without restraints. If you decide that a road isn't doing the job well, you can always dismantle it. In order to do that, click the icon marked '2' on the screen below. You will then be able to take a piece of the road (or the entire road) apart.
The roads are of course not free, and you will have to pay for them with wood. That's why you cannot just design the entire road system all at once - you have to do that on the fly, as the game goes on.