Welcome, Trail runner. Are you planning an overnight on the Mountaineers Route, or a day hike?
A day hike requires a Mt Whitney Main Trail day hike permit. While not ensured of getting one, your chances are pretty good if you plan on a mid-week hike. Those walk-in day hike permits become available at 2 PM the day before the hike.
If you are planning on an overnight hike, then you need a North Fork Lone Pine Creek wilderness permit. The quota is 10 per day, six available in advance, and four available at 11 AM the day before the hike. (Call to make sure of this!)
Since you have never hiked there before, I'd recommend the overnight, so you can pack in at a leisurely pace and camp; then next day complete the climb.
And be sure to acclimate!!! I can't stress this enough. You should get to altitude and stay immediately after you get your permits. Let us know more about your plans, and we can recommend some details.
For starters, read the "Wilderness Permit Options" link above on the left. And visit the Orientation Notes for first timers to read up on acclimatization, and find the Mountaineers Route link near the top.
