To build a new machine, you need to tap the icon with a saw on top of the screen and select the tab Machines. You will see your machines available and the requirements for the new ones.
 
Unlock a new machineTab Machines
 
Please note that you need to unlock all the previous machines first and upgrade their income level to 25.
 
Previous machine needed
 
Most likely, you also need to upgrade your sawmill.
 
New factory needed