Here is my approach to get a serial console on the Raspberry Pi: use a FTDI USB TTL-232R-3v3 cable with a 6-pin header!
The cable (e.g. from here, many alternatives available) translates
the 3.3 Volt signals of the Raspberry's header (GND, RXD, TXD) to a USB serial interface.
Just remember to cross-connect TX on the Raspberry header with RX on the FTDI cable's header.
I had the FTDI cable lying around, here are cheaper options!