How can I listen to Internet radio on my Sony PSP?

One of the many network-based capabilities of the Sony Playstation Portable (aka Sony PSP) that differentiates it from other handheld gaming devices like the Nintendo DS is that it lets you actually listen to streaming Internet radio broadcasts anywhere you can get an wifi Internet connection.
That’s quite a cool capability, as you might expect, and there are indeed hundreds of radio stations from around the world that you can tap if you know how to set things up and have the patience to pick the channel you want.
The first step on this journey is to ensure that you have a working Internet connection. Your best bet is to check out my own tutorial on how to set this up: Connect your Sony PSP to the Internet via wireless wifi.
Got that all up and working happily? Great!
Now you’ll want to click on the little “Home” button and get to the topmost level of the PSP menu system. Go the right as far as you can and you’ll be in the Internet area:

Use the up arrow to move to “Internet Radio”:

Now use the “X” button to select it and go deeper:

It’s kind of confusing. It says “About Internet Radio” but what it really should say is “Set Up Internet Radio”. Choose it by pressing the “X” button and, since you’ve already set up an Internet connection (If you haven’t, go back and review Set up an Internet connection on your PSP) the next thing you’ll see is the system negotiating that connection:

… and getting an IP address assigned by the network:

A few moments pass while the PSP loads in the Internet Radio starting page and you’ll see:

Now we’re getting somewhere!
Use the right arrow to select “Adding an Internet radio player”(you have to download the Internet radio “tuner” application to be able to actually listen to Internet radio. This means that, yes, you need enough space on your Memory Stick device to save the player):

Once you’ve pressed the “X” button to select that Web page link, you’ll be on a long page that shows you a bunch of different Internet radio tuner apps in a somewhat confusing manner:

What I find confusing at this point is that it’s not clear what’s different between the radio tuner applications offered from SHOUTcast (AOL) and ICECAST, and how to tell whether either the CLIP radio app or One Switch Radio app might work better for you, given that both are just different skins to the SHOUTcast network.
Ah well. Just pick one. I picked the first one, the default app for the SHOUTcast network. To do that, scroll down (use the down arrow) until you’ve selected the “Add the player to Memory Stick Duo media” link:

Push the “X” button to make it so and you’ll promptly be shown a ridiculously long disclaimer and terms of service:

scroll to the bottom of this page and choose “Accept” by highlighting it and then pushing the “X” button. Again.
Now the Sony PSP will start downloading the Internet radio player application:

You do want to save it, so highlight “Yes” and press “X” again. Now it’ll ask again for some obscure reason:

So, again, choose “Save” to continue and after a few moments (it’s a small file) you should see:

Then it writes the saved app onto your Memory Stick device itself:

Now, finally, you have a radio app on your Sony PSP. We’re done with this task, so press the “Home” button again and go back to the Internet Radio choice. This time it looks a bit different because the Internet radio player app shows up:

Nice! Select it by highlighting that selection then pressing the “X” button:

Presumably for your safety, you’ll find that you need to answer this question each and every time you launch the new Sony PSP Internet Radio app you’ve downloaded, rather a big hassle. Ah well, be that as it may, you can proceed by simply highlighting “Yes” and press the “X” button one-a more-a time.
Finally, the radio player should launch!

As you can see, the default radio channel it tuned was playing an Amy Winehouse song, Back to Black, when it started up. To change channels I’ll need to highlight one of the right arrow buttons adjacent to the “Reconect” button and step through, channel by channel, to find what I want.
That’s all there is to it. Now you’re officially a power Sony PSP user!
(even if that’s true, you might well find my other Sony PSP help quite useful too. Check it out!