From Frenchman Creek trailhead, make your way up a clear trail through dense forest. Grades are low and there are few roots or rocks. Pass two "no motor vehicle" signs. Take note of the second: there is a fork here. Continue up, but on the way down, stay on the smaller trail (from which you came).
Continue along the trail, crossing Frenchman Creek at tree line in another 10-15 minutes. At this point you are in a wide basin, with Mt. Columbia
to your left and Mt. Harvard
on the right. To summit the latter, continue through the basin on sometimes vague trail. Come to a grassy ridge, with the Harvard and Columbia
traverse to your left. Stay right, hooking up with the Harvard and Columbia
route to attain the summit of the former.
Head up and to the right on grassy slopes. The trail here isn't clear, but the summit is, so just walk toward it. Once at 13,800 ft, the ridge narrows and the trail becomes clearer. Scramble along some class 2+ rock formations (class 3 if you get bored) to attain the summit. Take note, Mt. Harvard
boasts an elevation of 14,420 ft, so it's a long way up.
From trees and wildflowers to marmots and pika, this route has it all. For some reason, the mountain goats up high are particularly sodium-deprived, to the point where they will follow you around just waiting for you to relieve yourself. The USFS has actually gone so far as to suggest hikers urinate on solid rock instead of dirt trail, thus discouraging these odd creatures from literally eating dirt.