If lost or destroyed, a new copy can be obtained from the bookcase in your Player-Owned House made through Construction.
When in your bookcase, this text is called Dwarf Multicannon Manual.
Below is the text you can read from within the book.
Constructing the cannon
To construct the cannon, firstly set down the base of the cannon firmly onto the ground. Next add the Dwarf stand to the cannon base. Then add the Barrels. Lastly add the Furnace, which powers the cannon. You should now have a fully set up Multi Cannon, to splat nasty creatures!
The ammo for the cannon is made from steel bars. Firstly you must heat up a steel bar in a furnace.
Now pour the molten steel into a cannon ammo mould. You should now have a ready to fire Multi cannon ball.
Firing the Cannon
The cannon will only fire when monsters are available to target. If you are carrying enough ammo the cannon will fire up to 30 rounds before it runs out and stops. The cannon will automatically target non friendly creatures.
Dwarf Cannon Warranty
If your cannon is stolen or has been lost, after or during being set up, the Dwarf engineer will replace the parts, however cannon parts that were given away or dropped will not be replaced for free. It is only possible to operate one cannon at a time. By order of the members of the noble Dwarven Black Guard.