See the Getting There section of the main page for directions to the trailhead.
Actually, this route page will encompass all the options of from the Government Mineral Spring Trailhead.
The shortest route to the summit from this trailhead is the Observation Peak Trail. From the trailhead go .9 miles on Trapper Creek Trail to a junction near a small stream for the Observation Peak Trail on the right. Take this trail for 2.5 miles up and around many ridges and creeks and past some neat waterfalls. Enjoy the old growth giants along the way.
At 2.5 miles, you will come to a side trail to the left, Big Slide Trail. This trail is a cut off trail that goes .7 miles back down to the Trapper Creek Trail. Stay right here (really straight) and continue up another 1.5 miles where the trail levels off slightly. You will come to another side trail to the left, another cutoff trail back down 1.6 miles to Trapper Creek Trail that is called Sunshine Trail. Continue on straight another 1.1 miles as the trail contours around the sub summit to the backside where there is a side trail to the left up to the summit. Take this route .6 mies to the summit.
Now, you can come back down the same way and hit one of those side trails that takes you back down to a couple spots along the Trapper Creek Trail. Or you can take a left when you get back down from the summit path and find the Trapper Creek Trail that came up from below. This route loops you back down some steep not-so-nice-as-you-came-up trail You will cross Trapper Creek up near a marsh that is its source. Slightly below that point is a Rim Trail side route to the left that will get you back to the Sunshine Trail although we never found it in the snow. The Trapper Creek Trail loops back down past a great viewpoint of Trapper Creek Falls before following the creek pretty flatly back to the trailhead.
Of note is the Deer Cutoff that falls between the Sunshine Trail and Big Slide Trail. It cuts off .4 of the trail but alot of it is going uphill and by this point, you are probably getting tired or sore and would give up the uphill for a better graded trail back.