I was very frustrated by the fog after quitting. I drank and drugged for 25 years, and in the last three or four, probably longer, though I didn't recognize it when it was happening, my cognitive abilities suffered significantly. They were slow to return, and I still have some impairment (as evidenced by memory and intelligence tests taken years ago and now). I did some permanent damage.
Looking back, I don't have crystal clear memories from my first six months or so sober. At a year, my memory still had not improved to the level it is currently--that probably took about two years. Working my brain seemed to help--doing crossword puzzles, sudoku, reading challenging texts, playing memory games (you can find some flash games in the arcade here). So did improving my diet and getting plenty of exercise, fresh air, and sleep.
I've heard as a guideline that it takes about a month for every year you drank/used for the brain to repair itself, though I wouldn't just sit around and wait. Be proactive.
Also, if you find yourself having difficulty not drinking, remember that putting alcohol (any drug) into your body resets the detoxification clock. If you can't stay sober on your own, I'd suggest going to an AA meeting to see if you identify. Alcoholics usually don't do well staying sober on good intentions alone.
Peace & Love,
Sugah