The Alchemy Engine is the second construct listed under the "Science" tab.
You can build it using 4 Boards, 2 Cut Stone, and 2 Electrical Doodads.
Boards and Cut Stone are built using logs and rocks and are located in the "Refine" tab.
Electrical Doodads are built using Cut Stone and Gold Nuggets and are located under the "Science tab". You will need to already have a Science Machine (4 rocks, 4 logs, and 1 gold nugget).
So in total you will need:
16 rocks
20 logs
5 gold nuggets