For my own benefit, and the benefit of anyone Googling for this...
Go into Phone Settings -> Connectivity -> USB connection mode, and choose Data Service
Plug the phone into your computer using the USB cable (presumably Bluetooth will work as well, but USB should be a lot more reliable)
Download the
LG Mobile Support Tool. This tool is primarily for flashing your phone's firmware, but it also contains a handy link to download the USB modem driver.
Once the tool is downloaded, run the installer and wait for the tool to appear. If it doesn't, it can be found on the Start Menu under LGMobile Support Tool.
In the tool, go to the Customer Support menu, and click 'Application, Manual and USB Driver Download'. You'll need to put in the phone's IMEI or model/SN, both of which can be found beneath the battery - in my case, the IMEI wasn't recognised but the model and serial number were.
Once the phone is recognised, double-click the usb modem driver to download it. It will be saved to C:\KU990\ as something like "LGUSBModemDriver_(version details).exe". Install the driver.
Once that's done, plug in the phone with the USB cable, and your computer should recognise it as a modem. Go into Device Manager (Control Panel -> Hardware and Sound -> Device Manager), look under Modems, and double-click your LG modem (mine was called "LGE Mobile USB Modem").
Go to the Diagnostics tab and hit Query Modem. The modem should reply with a bunch of diagnostic messages. If this works, go to the Advanced tab and enter the following into the 'Extra initialization commands' field:
+CGDCONT=1,"IP","orangeinternet"
Now create a new dial-up networking connection. In Windows 7, you'll need to go to the Control Panel and open the Network and Sharing Center, then click 'Set up a new connection or network'. Follow the wizard, creating a dial-up connection. If you have more than one modem now (most laptops have a built-in one), you'll need to select to use the LG USB modem.
When setting up the connection, you'll want to leave the username and password fields blank, and enter the phone number as:
*99***1#
Finally, connect to the new dial-up connection and try loading something (if you're testing this out, make sure to switch your wireless connection off or unplug your ethernet cable first ;) )