I've been up the North Fork of Lone Pine Creek and the MR several times over the last ~5 years and made mistakes each time. In addition to the links posted, here is what I wish I knew the first time:
Bring a helmet and micro spikes.
When you get to the Lone Pine Creek crossing, look up sharply to the right. That is the trail that leads to the MR. Some people end up bush whacking to find it. ~2 years ago the Friends of Inyo NF cleaned up this part of the use trail.
Crossing the E-Ledges be careful not to go too far. The rangers sometimes put logs where you should not go, and put cairns to show the way. Don't count on these being there, though, as some hikers intentionally knock down cairns. Take your time on the ledges to find a safe way to climb up. There is at least one YouTube video that shows someone going too far along the first ledge.
Above the ledges stay to the right near the side of the mountain, not through the trees by the cliff's edge.
The AllTrails smart phone app can be helpful. Have this route loaded well before you enter the trail.
At Lower Boy Scout Lake you can easily lose the use trail to the left near a giant rock field. You can pick up the use trail if you are patient crossing the rocks about ~10M from the lake. This area is where I have wasted the most time, especially if there is snow.
Between LBSL and Upper BSL you will need to find the best creek crossing. There is a certain big rock that you should look for. Check the pictures in the links above. There are two creek flows to cross. If you miss this you will waste a lot of time getting back on the main route.
Near UBSL is where the Whitney Zone map (the one that includes this area) shows the MR starting. You will have gained much altitude by this point. Many people can make it to this spot in ~3-4 hours under ideal conditions. I find the MR easy to lose, so I take my time and check the map often. Some foot prints may go off the route. These may be from climbers ascending from another way.
When you finally get to the lake and look up the chute, notice the big discolored rocks to the left. They are easier to climb than scrambling up the scree near the bottom. Eventually, there is a way to traverse over to the chute and climb to the notch.
[I'll skip the final 400 as there is plenty of good advice here, except to say stay the hell away from the 'easy walk off' option, even in August. Just my opinion.]
On the way back, below the E-Ledges, don't follow the trampled brush along the side of the mountain. Cross the creek below the water fall (the way you came up). That seems like it would be obvious, but it is easy to miss this. A couple of years ago I encountered someone who was way out on ledges below the E-Ledges (because I started to make the same mistake). I helped him back.
Also, don't expect to see many people on this route.
