Assuming you have the Uno boot loader on the Atmega 328, and it is wired like an Uno (with a 16MHz crystal etc) then it works a lot like a pro mini. Just connect the USB to serial converter (in this case the CH340) to the chip. Connect it like the Shrimp here.
Well as you sold my original setup to me through your eBay shop, and incidentally I will come again as I have, then I know, you know that you know, that I know [d'you like that] just what your talking about and the CH340 certainly sets itself up straight out of the box; there is nothing like the driver problems which can be faced by the FTChip, chip. Advice for which I shall remain grateful and for your taking me down that route. Incidentally Arduino suggest that you do not use the UNO for these purposes and suggests the Duamilanove instead.
I have to confess that even though I have the knowledge of the CH430 I haven't wired it up to my stand alone as I have been following Tutorials [is this where I've gone wrong], although I have made mine multi-purpose in so much as it can bootload, program alone, program as an (Arduino Prototype V.5) shield and act as a working proto., board too. So now I'm off to see if it will turn my somewhat recalcitrant proto., board in to a fully fledged grown up one ........................... here's hoping.
One further little grumble; nobody seems to tell us newbies, is that you can only use Rx to Tx when the Atmel Chip caries a boot loader; else it has to be the in-circuit peripheral method.