Hi HP, I live at 300' elevation, here's what I do that works for me:
Drive to Horseshoe Meadows and spend a night inside my car, or on the ground at the walk-in campground. Do whichever is easier. Take half a 125 mg Diamox (Rx required) tablet that morning, and again at night. Makes you pee more, so expect that. Continue taking it for at least 3 days.
Next morning, drive down to Lone Pine and get breakfast. Take another half-tablet of Diamox. Drive up to Whitney Portal and haul the overnight pack up to Trail Camp, 12000'. More sensitive people could and camp at Outpost Camp, 10,000'.
Third day actually climb to the summit. Return to camp, spend another night, unless you have enough time and strength to hike out.
If you're day-hiking, spend the first night at Horseshoe Meadows (and maybe more time that day). The second night at the Whitney Portal walk-in campground, wake up at 3 AM and go for it. But make noon your turn-around time. I saw too many people forgetting that rule, and looking at hiking down in the dark for hours.