We will not go deep into this subject. We are not doctors and there is extensive literature on alpine medicine available.
You should educate yourself and also read and bring with you the book "Medicine for mountaineering (The mountaineers) on the expedition. We would however like to share with you some of our own hands-on experience. Our advice is out of a climber's perspective, a practical supplement to conventional medical knowledge.
There is no need to hurry or exert your self while acclimatizing. You shouldn't climb higher than 300-500 meters/900-1500 ft per day. That's not very hard to do and you might be tempted to go farther. But all it will bring you is headache, sleeplessness and possibly mountain illness in the morning. Use your head, not your legs only.
These are the signs to watch for when climbing:
This is serious. Cerebral and Pulmonary Edema are caused by fluid collecting inside the brain and/or lungs.
Cerebral edema shows as failure of motor function, vomiting, hallucinations, extreme sleepiness and ataxia (can't walk heel to toe). Try to walk a straight line or point your nose if you suspect it.
Oxygen, Gamow bag-treatment, Diamox and Decadron are helpful, but the most important is rapid descent.
The same treatment counts for Pulmonary edema (blue lips, very heavy breathing, gurgling sound when breathing).
Both HACE and HAPE arrive upon pushing in spite of AMS. They are the immediate result of too much, too fast and a general negligence to the body's subtle or in the end, not so subtle warnings.
Sometimes we have to push the limits. Storms and other acute situations might force us into circumstances that we don't like. That's one thing. But to come up with AMS due to impatience and ignorance is sad. It could cost you your life. HAPE and HACE kill fast.
Lastly, never cook inside a sealed tent. The gas withdraws the oxygen from the air and this can cause HACE/HAPE conditions in your sleep.