Essentially, we make a huge tapering hole in the ground, with each "tier" being part of the roadway for trucks and other mining equipment.
Light isn't really an issue, except at the very bottom, but even it receives some light during the day. Moving the dirt isn't a problem either - I'm not sure where it goes, but the tailings end up somewhere (it isn't all consumed in the mining operation).
As far as a view? Well - if such a construction was done for housing, the tiers could be rows and rows of buildings hugging the sides of the pit, potentially looking out and over at other buildings across a large expanse - like looking out over a valley (if you've never been to a deep pit mine, take a trip to one sometime - it's quite amazing). With trees, plants, etc - perhaps water features and maybe a lake at the bottom - I think (in theory) it could be quite lovely to look at and live in.
It would be nice if the deep pit mines we already have dug could be repurposed, but the problem with many are the amount of contamination caused by the mining and other activities during the operation of the mine; I doubt it would or could ever be fit to live in. Some of these mines are backfilled with the tailings afterward, but not all.