They say it is good for brain fog because of the action it has on glutathione, an amino acid that has to be created by the body within cells. It has a lot to do wtih how fats get utilized. The recommended dose is 50-100 mg. Overdosing is not smart.
It totally depends on WHy you have brainfog. If you can rule out toxicity and healing crisis and low thyroid - which you can only rule out IF you are drinking 50+ ounces of filtered water and doing colonic irrigations or enemas very very frequently and have had your TSH checked, then really the next step is to take in good healthy oils and digestive enzymes to make sure you are digesting those oils. ALA is a good option to try, as is Taurine, Arginine.
If your blood tests show adequate amounts of lymphocytes, then chances are you do NOT need to supplement with ALA.