How can I set the track width for a net?

Track width can be defined at the schematic design stage for use by the autorouter or assist while manual routing.

Starting with a schematic populated with components, as you start placing the net, use a right click and select "Change Net" (or shortcut SHIFT+N) and then change the "Net Class" for the track widths you require on the PCB. Note that the final track width will be assigned on the PCB from the PCB technology, it is not defined from within the schematic.

This simple design has the nets defined as shown in the schematic design technology (SHIFT+T).

Next, translate to a PCB as normal and place the components.

Launch the Autorouter. For simple designs such as this, where a bias to the track routing on the copper layers is not important, set this to "Unrestricted", which allows tracks in any direction on each layer to avoid vias being placed and the track swapping layers at each change in direction.
Then click "Route".

The tracks are routed with the appropriate track widths defined for Power and Signal Norm in the design technology. The track width can be confirmed by examining the properties. Below shows the placed signal and power tracks.