What is the trouble? Booze is booze and dwarves will be happy even with the lowest quality swill.
All it takes is plant gathering or farming and brewing and building a still. Booze can be made from underground or aboveground plants.
The only time you shouldnt be able to make your own is if your biome doesnt support any farming, in which case you are kinda screwed anyway lol.
No booze is bad, no booze and only murky water is worse. Murky water can be countered by placing a well above the water, which somehow makes it a lot more tolerable to them and they do not get the murky unhappiness. No booze and only murky water is going to make your fortress go downhill in a hurry.
To farm you need plump helmet spawn, some underground room that isnt stone. Build a farming plot by hitting b and then p and then the umkh keys to expand the plot to the size of the room. Once the plot is built by a farmer skilled dwarf then you hit q, target the plot and then hit s to set up the plot to have crops in spring through winter.