There are two ways to get to Larch Lake: either up the Chiwaukum Creek trail to a junction with the trail to Larch Lake, or via Alpine Lakes High Camp (reservations required).The coordinates provided are for the Chiwaukum Creek Trail route.
Chiwaukum Creek offers a long meandering hike of 24+ miles round trip (12 miles one-way), great for overnighting. Follow the Chiwaukum Creek trail for around 6 miles where it meets the North Fork Chiwaukum Trail. An additional 6.2 miles on that trail will take you to Larch Lake.
As mentioned above, the Alpine Lakes High Camp offers a shorter route, with a hot shower at the end, but one you do need to make reservations for.