Shadowing is a way to increase your listening comprehension, better your pronunciation, and give you more natural pitch and rhythm in your foreign language. All you need is:
1. A text in a foreign language.
2. The same text in your native language (for our purposes, English).
3. Audio of the text (in the foreign language, of course).
You can find a more in-depth discussion of Alexander Arguelles' specific technique of shadowing here or here. The following is just a basic run-down.
For beginning students, try listening to the audio without looking at the text. Your goal is to repeat the audio as closely as possible. This means you will be speaking while the audio is going, maybe a second or two behind. Try to honestly rely on your listening ability. Don't worry if you don't know the exact meaning of the words you say, because you will be learning them shortly. Next, you can listen to the audio and read silently along with text 1. Then listen and read silently along with text 2. Finally, you can return to shadowing, following along with the text. Even though you are reading, your goal isn't to read the text; rather, you want to hear the audio and repeat it, following along as a supplement.
If you are sufficiently advanced, you may not feel the need for the texts. I don't consider myself sufficiently advanced, but I try to shadow as I watch dramas, which, naturally, I don't usually have the text for, unless there are subtitles 字幕 attached. Shadowing dramas is definitely not the easiest task, since half the time people are talking over each other. You may want to try watching the drama first, since shadowing it can sometimes take a bit of the enjoyment out of it. This means you'll have to find a drama you don't mind watching twice. If you are at loss as to where to find dramas, try one of the links on the side bar. Because you don't have a text to refer to in order to perfectly parse or understand every word or grammar point, you may find shadowing a drama to primarily improve your listening comprehension, pronunciation, and rhythm, less so than up your grammar/vocabulary (although context is one of the most effective teachers of grammar/vocab, I think).
You can use the dialogues and corresponding audio tracks from your textbook to practice shadowing. This is probably the best course of action as a beginner, since dialogues from textbooks are usually more clearly enunciated and a bit slower than normal speech.These are the kind of text/audio sources that Alexander Arguelles seems to be using.
Another option: audiobooks! You can find a large repository of them here and here. Most of them also contain transcripts. While this may not allow you to have a completely natural cadence (reading cadence is often quite different from a natural speaking cadence), you will definitely see improvement in your pronunciation and listening ability. Listening to audiobooks will also prepare you for the kind of constructions you may come across while reading.
Try looking at Alexander Arguelles' website. The previous link will send you to a section for self-study aids, but if you're interested in languages, I think it's a good site to peruse for a bit of time!