Details
Take the Taylor River Trail and go to the end, approximately 6 miles. This is relatively easy, but the miles and hours will take a toll.
The trail ends abruptly at the edge of the Taylor River, now reduced to a manageable creek. You will need to ford here, cold but rarely difficult. Find the trail on the other side and continue, the grade soon becoming steeper and entering an unending sequence of short switchbacks. At 0.9 miles, cross a small creek on solid rock at the edge of an interesting "skeeter bathtub" pool. On the other side, the switchbacks continue with a vengeance, generally tracking the creek uphill. At about 1.8 miles, the trail veers away from the creek to the southwest and the grade moderates, following a bench to the southwest. At about 2.3 miles, reach a rockfall with rough but stable broken boulders.
Here's a small mystery for you. Older USGS maps show the trail continuing along the bench on the other side of the rockfall, about a quarter mile, then generally following a rounded ridge to the southeast, arriving at the west shore of the lake. Maybe this was the main route in pre-wilderness days, but I have never found it. Is it still there? Could it be a viable alternative to the main trail?
The official trail veers sharply left to scramble perhaps 100 feet up the boulders. This is hardly a show-stopper, but it slows things a little. Once at the top, the trail resumes a relatively gentle grade, passes through a smooth gap at the top of the ridge, and then ramps gradually down to the lake.

There is one camp site here where trail meets lake at the northwest corner. There are some large but friendly boulders around the north lake shore to the left, reasonably appealing as a fishing platform even if fish are rarities. Perhaps a better plan is to pick your way along the lake shoreline in the other direction, down the edge of the west shore on gravel. Scramble up and over a crooked tree, and drop into a fold on the other side. There is a cute spot in the back of this gap suitable for a small primitive camp. Or, locate the distinct foot path leading sharply up the other side of the gap, and follow 1/10 mile to a wide-open but brushy area near the lake outlet on the west shore. This would probably be preferable for bigger camps. This area was once privately held, including a cabin, but when the Alpine Lakes area was set up, the land was donated to public service. Even the usually cynical RidgeRat gives a grudging nod of admiration. Only a historical site marker remains.
Base campers can take off from here to scramble to higher, smaller, and I would say more interesting small lakes in the Green Ridge area. Rock Lake shows as a seasonal lake on older USGS maps, but I have never seen it go dry. Lunker Lake is a cute lake but contains nothing resembling lunkers. HiLo Lake has a unique contoured shoreline reflecting the drastic changes in seasonal water levels. An overly-elaborate miner camp can be found at Green Ridge Lake.