From the South (Carrigain Bowl): 2 options: approach The Captain from the Left or Right. As Frodo and Hamtero said, if you swing to the left of the Captain you end up in the Hancock/Captain col and you basically have to get lucky about picking a route. Some parts are ok other parts are horrible. There is a creek in the col but as I recall, on the right side (E) of the creek the trees are, in my opinion, impenetrable. I've never seen trees that I felt like I couldn't even push through if I tried.
Approaching The Captain from the right side of the Bowl: you'll have to start slabbing along the bulk of Carrigain early on to avoid the cliffs... I don't know what the woods are like there and I suspect that this is not a common route. However, the area just South of the pond but North of the cliffs is actually ok. On one failed attempt we headed South from the pond but were stopped by the cliffs... and then essentially followed the (imagined)
Wilderness Boundary to Carrigain Summit. The woods were fairly tame. The areas North, West and East of the pond, however, is horrible.
Don't approach from Desolation unless you're planning on a long day. There are some very grown up logging roads that will be impossible to follow in the snow. Although maybe following Carrigain Brook, if it's frozen, could be a viable option. The woods surrounding, in that entire area, is pretty terrible.
NH_Mtn_Hiker did a few hikes from Hancock to The Captain -- do a search for those trip reports.
Approaching from Carrigain is easy but a little tricky probably in terms of navigation... if you wander off course you might end up somewhere bad. However, going from the Captain (or the pond) as I mentioned already is pretty easy.
-Dr. Wu