Some silver chains are mad by hand with individual wire links that are formed, linked and soldered together. However, most silver chains are machine made by a series of operations. First wire is drawn to the proper thickness or gauge and annealed for workability. It is then fed into various types of machines that form links of certain shapes in a pattern and connect them together. Finally, a soldering operation fuses the links together so they are secure. Chain is made in continuous lengths on spools. Later, different machines will cut chain to specific lengths and connect the jump rings and clasps to create finished necklaces. There are many differend chain styles. The reference link below provides more details.