How do I make vehicles faster?

Vehicles are the fastest troop type. You should do the research for each APC to increase the marching speed if you haven't already.

If you are a Farmer class then you will have a 30% combat march speed reduction so if the speed is important to you then consider changing.

For some marches you can invest in March speed up items that let you increase speed by 25% or 50%. These can be stacked as well. They do not apply to all marches though.

You should work on crafting parts in the parts factory. The basic trailblazer set has parts that can speed up marches to gather. But the Phantom set has parts that will increase the vehicles general marching speed.