This is the route I imagine most people mean when they refer to approaching Mount Wood from Mystic Lake. It climbs from Mystic Lake into the hanging valley on the southwest side of the mountain and then climbs up to the southwest ridge and on to the summit. In total it is roughly a 20 mile round trip with about 6000 feet of elevation gain from the parking lot at the West Rosebud trailhead. My friend and I did this very slowly over the course of 4 days but I imagine it could be done overnight with two fairly strenuous days or in 3 days with more ease. If you're making a one-day ascent the direct route from the parking lot is probably better. Although the distance is short, roughly half of it is off trail encompassing most of the elevation gain, so don't expect to blow through this like you might a similar distance on trail. The climbing is fairly easy and non-technical but the route does require significant off-trail travel and decent route-finding ability.
Drive to the West Rosebud trailhead (directions on the main Mount Wood page).
From the trailhead hike up the road and follow signs through the housing area to the trail that goes to the lake. Follow this trail around to the west end of mystic lake (the lower of the two lakes in the valley). At this point leave the trail and head north (right side of the trail) to the creek connecting island lake and mystic lake. Ford or hop across on logs to reach a number of excellent camping sites on the other side.
The west end of mystic lake
In the meadow in the hanging valley, the view to granite peak is excellent
From here head northeast through the forest remaining on the flatter terrain near the lake until you reach the stream which drops down from the Southwest drainage. Cross the stream and turn north proceeding directly up the steep slope through the trees. Although forested, there is very little undergrowth, the main obstacles being the occasional downed tree. On the way up try to stay between the stream and the small ravine to the east (right). At the top of the slope the forest thins and you'll enter a hanging valley. Continue up the valley through a mix of sparse trees and moraines (the going here is a little slow). About 3/4 of a mile from the top of the steep slope up from the lake you should enter a large meadow with several small streams running through it. This is a good place to camp for a relatively short summit day.
Route through the valley and up to the ridge
From the meadow you will want to climb up the large slope to the east to gain the plateau southwest of the peak. A small tip: the slope directly above the meadow is steep brushy and frustrating. Head about 1/4 mile further up the valley before starting up the slope. The slope is rocky and can be rough going in places but is generally walkable. At the top turn to the northwest and proceed uphill along the wide, flat ridge toward the peak (which should be visible in good weather). After roughly a mile the ridge narrows to a thin exposed scramble. You can proceed along the ridge all the way to the summit.
View down to the upper lake from the climb to the summit
West Summit from the upper lake
A less exposed option is to drop down to the upper lake in the bowl below the peaks either by sliding down the snowfield or walking around it's east side. When I was here in late August 2010, the snowfield extended all the way up and onto the southwest ridge so that traveling directly up the ridge would require scrambling on snow at the edge of a steep snowfield. We opted for this second option rather than risk sliding 500 feet down the 30 degree snowfield into the rocks around the lake. From the lake pick your way up through the steep talus toward the west summit 850 feet above. The bowl steepens near the top and depending on your specific line may require some class 3 moves. From the west summit I suppose one could traverse along the ridge to the east summit (though I have not attempted this).
Just the normal gear you would bring for a couple days backpacking. Be sure you have good rain gear. A GPS can also be useful on the featureless plateau when the weather closes in (it was helpful, but not vital, in this context for us). This is bear country so make sure you have equipment for proper food storage (I recommend canisters if you plan on camping in the hanging valley as the trees are mostly too small to hang food).
A storm closes in from the west early in the morning
There are no major technical hazards on this route but the weather is unpredictable. You can get the forecast at the ranger station in Red Lodge but don't count on it. Expect thunderstorms in the afternoon and don't be surprised if remnant storms from the previous day further west strike early in the morning. Start out for the summit early enough to be down off the ridge and plateau and back in the hanging valley by the early afternoon to reduce the risk of lightning.