To enable the Command Console you first need to do some tweaking in your settings.ini of your save. This can be found in the [donotstarve] folder, If you don't know where it is by default the location is in your documents folder, Locate the settings.ini and open it with notepad or notepad++ and where it says [MISC]ENABLECONSOLE = false and rewrite it as [MISC]ENABLECONSOLE = true then save the document.
Then to open the console while in game by pressing ~, ^, ø or ö, Ctrl+Ñ, depending on which keyboard layout you have. Also you can hide the console menu again by pressing Ctrl + L.
Note: You have to re-enter every command after loading a world.