Serial communication with a DIY Arduino remains a topic of interest as the USB connection with an FTDI chip is not always easy to DIY.
A MAX232 as shown before can do the job and so can a few discrete components. But if you have 2 gates left in e.g. a 7404 (a HEX inverter) you can use that one too:
If you have 3 gates left, you could add one to the above circuit to transfer the DTR signal of pin 4 (on a DB9) to use that as a Reset for the DIY Arduino. Just make sure you feed that signal to the input of a spare gate via a voltage divider (2x10K).