Bitbang ATMega-328PU with CT210x using avrdude
Has your AVR been programmed with the Arduino bootloader before?
If not, see "Bootloading your chips" on the site you linked to.


Please note that there are different ways to program a bare AVR and an "Arduino":

The bare AVR does not have a booloader pre-installed. Therefore, it can only be programmed via an AVR in-circuit programmer (ISP) (hardware!). This uses the RESET, MISO, MOSI, and SCK pins (see the "Bootloading" section). avrdude can then be used for example to upload the bootloader.

Quote: "if you purchased some extra Atmega8 or Atmega168 chips from an online store they will have NOT been bootloaded with the Arduino bootloader (with the exception of Adafruit Industries). [...] You won't be able to program your chips using the USB to serial breakout board and the Arduino software [...]"

Only after the AVR has been set up with the Arduino bootloader can it be programmed via the USB-to-Serial adapter you already have. This connects to the TXD and RXD pins (and possibly also to the RESET pin).

Quote: "Connect the RX (pin 2) of your Atmega chip to the TX of the USB to serial board, and connect the TX (pin 3) of your Atmega chip to the RX of the USB to serial board."