I'm struggling a bit to find relevant documentation on this subject when it comes to using just assembly. All I've found is either irrelevant or for BASIC. My goal is to be able to send and receive strings from the C64 IEC serial port, but I cannot find literally any documentation on kernal subroutines, instructions, or examples. The documentation on the IEC serial port is useful for seeing how it works in terms of electronics, but I either found it too difficult to parse or there's no information on programming it with assembly.
The IEC kernal (sic!) routines can be found at $ed00, and the RS232 kernal routines at $eeba. Michael Steil has built a very nice side-by-side table of 5 different commented disassemblies which, taken together, should tell you everything you need to know.