If you remove a bearing wall without providing replacement support, you threaten the integrity of the house itself. All exterior walls are load-bearing, as are many that run lengthwise through a house. But there can be others. It can be as easy as heading to the attic to see if any joists, beams or rafters rest on the wall. Or it can be a lot more complicated.
Actual demolition begins with removing drywall.
This is done carefully and sytematically to avoid damaging existing plumbing, ducting and wiring. Depending on the plans, these utilities will be capped off or rerouted. In the case of a bearing wall, temporary walls have to be nailed in place beneath ceiling joists on either side of the wall. Then the studs and bottom and top plates are removed. Finally, new support posts and a header are installed.