The short answer: very extensive systems of phonetic shorthand, a special keyboard with very few keys designed for chorded input (multiple keys pressed simultaneously), and specialised software dictionaries to translate the shorthand back into English. Professional stenographers can type upward of 300wpm as standard. The downside is that it takes years to become proficient. http://www.openstenoproject.org/ is an interesting resource if you're curious.

They don't type in conventional English, they type in shorthand.

"The stenotype keyboard has far fewer keys than a conventional alphanumeric keyboard. Multiple keys are pressed simultaneously (known as "chording" or "stroking") to spell out whole syllables, words, and phrases with a single hand motion. This system makes real-time transcription practical for court reporting and live closed captioning. Because the keyboard does not contain all the letters of the English alphabet, letter combinations are substituted for the missing letters. There are several schools of thought on how to record various sounds, such as the StenEd, Phoenix, and Magnum Steno theories."

https://en.wikipedia.org/wiki/Stenotype#Example