You can listen to radio stations that stream over the Internet by using specialized home audio devices that are now available. In general, these devices will allow you to listen to Internet streaming audio, and other audio, on your home stereo system, boombox, set of powered speakers, or headphones. The challenge is that there are many slightly different devices for sale, and it can be a challenge to understand exactly what they do -- and don't do -- from their descriptions (written by marketing departments, I guess). And though, if you see a "microwave oven" or "toaster" advertised you know pretty much what to expect, there are (as yet) no standard names to help distinguish these very different systems from each other. I will do the best I can in a few paragraphs.
You can use the amazon.com widget at right to search amazon.com for these and similar Internet audio devices that meet your needs. Change the search term as you see fit, then press the Go button. I suggest trying these search terms in this widget. You never know what might turn up.
One type of device might be called a "Wi-Fi radio" or "Internet radio". This device has its own built-in speakers, and it might look just like a standard AM-FM radio on your nightstand or bookshelf. Rather than receive radio waves from local broadcast stations, it connects to the Internet through an available WiFi network (you must be able to log in), and it plays Internet audio streams through its own mono or stereo speakers. Some of these devices may require a computer to set up, but they don't require a connection to a computer to operate. On the other hand, these devices may be limited to playing audio from Internet streams; they may not be able to play audio you may have stored on your computer or MP3 player.
An "Internet radio adapter" or "Internet radio tuner" (again, there is little agreement on what to call these things) is similar except that it does not contain its own speakers. Instead, you connect your existing audio system, powered speakers, or headphones to this device with a cable. You may prefer this type of device to a WiFi radio if you already have the audio system you want to use and need only a way to supply it with Internet audio streams. As with a Wi-Fi radio, this device connects to the Internet through a WiFi network, and it can't play audio you may have stored on your computer or MP3 player.
Similar to these tuners or adapters are devices that wirelessly distribute audio -- any audio -- from your computer or audio device to one or more nearby audio systems or sets of powered speakers. With these systems, one unit in the system is connected (usually by USB cable) to your computer and another unit is connected by audio cable to your nearby audio system. These systems will not themselves connect to the Internet. But if your computer is receiving an Internet audio stream, you can listen to the stream there at your computer and also on your nearby audio system, powered speakers, or headphones. No WiFi network is required because this system creates its own wireless network. You can also use such systems to play audio already stored on your local media (including your computer or MP3 player) even without an Internet connection. Some of these systems can be used with more than one receiver, so you can hear your audio in three or more places in your home.