How do I set up a network in Windows 98?

Microsoft's removal of non-plug-and-play drivers on the Windows Me installation CD led to further confusion when many older modems, sound cards and network cards appeared not to be supported as they were after a Windows 98 installation. In many cases, this could be remedied by manually installing the proper driver(s). However, due to the aforementioned lack of real mode support, hardware having only real-mode drivers is incompatible with Windows Me.