It's a long slog, but worth it in the end. I did this hike in one day and summited in about 4 and a half hours, although talking to others at the top, 7 hours seemed more common. I overpacked, bringing more clothing and liquid than I needed, but better safe than sorry on a mountain this high. The hike is much longer than it is steep, only gaining an average of about 550' per mile. But the altitude can get you, and drinking and eating plenty along the way is important. I did it on a crystal clear day and the visibility was unlimited. It was rather crowded at the top for a Wednesday, with people ranging in age from 7 to 71.
I drove down from Seattle and didn't have a permit. But I stopped in to the interagency office just south of Lone Pine the day before and was able to get one no problem. No-shows and cancellations mean that some walk-up permits become available, but you have to get to the office the day before you plan to hike. Also, if you're staying overnight or hiking on the weekend, getting a walk-up permit will be tougher. And be careful not to leave any food or food residue in your car, even for a day hike because bears will break into your vehicle. Either rent a bear canister or leave your stuff at the Whitney Portal hostel in Lone Pine.
The trail is well-maintained and at times beautiful. You pass several tarns and once along the crest trail, you get peeks through the spires toward Lone Pine. You'll earn your buffalo burger at the Mt. Whitney restaurant after this one.