I’ve only done this twice so hopefully you’ll get a second opinion here.
Go south on Interstate 15 to west Route 160, “Blue Diamond Road” (to Pahrump). Follow to Pahrump and watch for Bell Vista Avenue, 2/3 through the town. Turn left (west) and stay on the road (it changes to Ash Meadows Road while Bell Vista continues off to the right). It should be a natural choice; I’ve never noticed that it stopped being Bell Vista.
This will take you to State Line Road. Turn left on State Line. This will take you to the tiny town of Death Valley Junction. At the T, go right for a very short jog then go west on Route 190. You stay on Route 190 all the way through Death Valley; past Zabriskie Point, Furnace Creek, Stovepipe Wells and Panamint Springs. It’s a big long looping drive and Death Valley is aptly named.
After Panamint Springs, it’s another fairly long drive to where Route 190 turns south around the remains of Owens Lake and Route 136 takes the north way around it. Take Route 136 north to Lone Pine, and look for the Whitney Portal Road in the middle of the town. Turn left and follow to the portal.
If you really intend this to be a day trip (returning to LV that same day), be prepared for a very long, very arduous day. Seriously.