Having trouble Uploading code to working Arduino Pro Mini

I have written a large project in C and want to upload this to an Arduino Pro Mini using an FT232RL FTDI serial adaptor to upload the code onto it.
I have attached all of the pins as needed so that the code can be uploaded to the pro mini, but the computer is not picking up the port that it is connected to and will refuse to connect to the computer.

There are three lights that I can see when the device is plugged into the computer, one red LED on the FT232RL and then one red one that is constantly on with a green one that flashes when plugged in on the Pro Mini.

I don't know what I am doing wrong or how I would fix the problem.

Are you using Windows? If so the USB-Serial adapter should show up in Device Manager when you plug it in, even without the Pro Mini attached. Check that as a starting point.

I am on windows and the USB serial adapter isn't showing then.
I have installed the driver for it and it still doesn't show.

And Windows doesn't play a sound when you plug in or unplug your USB-Serial adapter? There are a couple of things you could try to narrow down the issue:

  1. Try a different USB port on the computer. Or, if you're using a USB hub, try removing that and plugging the USB-Serial adapter cable straight into the USB port on the computer.
  2. Try a different cable. USB cables can get damaged, and some cables that are only meant for charging devices don't actually have data wires.
  3. Try the USB-Serial adapter on a different computer. You don't need to go to the bother of installing the drivers- you're just looking to see if it shows up in Device Manager as an unknown device.

If none of those give any results then I expect you have a dud USB-Serial adapter.