Please allow me to expand on the other answer you recieved a little, as far as it regards transport category aircraft:
The fuselage, wings, plyons, and stabizilers are all assembled separately in different parts of the world.
The frames and stringers for the fuselage are held in 'jigs' and fastened together, and the the outer skin is RIVETED on, not welded. There may be some high-strength steel fastners inserted (called HiLoks) occasionally, but the vast majority of the fastners are alluminum alloy. The fuselage is actually made in sections of between 10 and 40 ft long called 'plugs'. These plugs are shipped to the assembly factory (for Boeing, in either Everett or Redmond (?)).
The wings and stabilizers are assembled in much the same fashion. The framework of spars and ribs is assembled first, then skinned, much like the fuselage.
The plugs, wings, and other major structures arrive at the factory with wiring and pumbing for hydraulics already installed. The final assembly consists of lining up the plugs, wing assembly, and then the stabilizers, and attaching the parts. Then the pylons and landing gear are installed, and the interior is finished off.
I am going to Boeing in Seattle on the 24th to begin a seven week 767-400 school. It will include several trips to the factory and flight line. I'll be glad to post more about this entire process as I get to see it first hand!