Hi Switch, just a couple of days ago, I too bought a Wifi router. I an totally unaware iof what the process is for a USB adapter, but I think I can give you a general idea of it:
1. Install the drivers and plug the USB adapter.
2. A new connection may appear in your "Network connections".
3. Enable that new connection.
4. You may need to configure the Wifi network such as its SSID, security settings, WAN settings, etc. This can be done by opening your browser and typing the URL given in the instruction manual. in my case it was *192.168.1.1. Other possible values for this URL are:
10.x.x.x
172.16.x.x
192.168.x.x
So search for something matching this pattern in the instruction manual.
It will also have a username and password, the default values of which may be given in the instruction manual.
Enable WER/WAP or other security measure to secure your Wifi.
Now, search for wireless networks on ur PSP. Connect to your Wifi network and now you can share the internet.
Remember, this is just a guess....I have translated my WIFI router installation into USB adapter experience