In smaller aircraft, the baggage is put directly inside the cargo hold.
In case of larger aircraft, the baggage is put inside the conformal cargo container or the unit load device, which is then placed inside the cargo hold.
On a modern large airliner (particularly for long haul), the bags are loaded into a ULD (Unit Load Device) which are the big silver boxes that you see on airport ramps. These ULDs are then loaded into the cargo hold of the aircraft, which is located directly below the passenger deck.
Here is a photo of the empty cargo hold of an A320 (source):
And this is what it looks like in cross-section after loading (this is an A300) (source):