The APIs in the original examples paired with this PDF have changed, and I decided to do some different things with the code and/or circuits, but the original code can be found here.

Temperature and humidity sensor served on a web page within the local network.

Dependencies

You need to install a couple of libraries for this project:

The DHT and the Adafruit Unified Sensor Driver libraries to read from the DHT sensor.
ESPAsyncWebServer and Async TCP libraries to build the asynchronous web server.

The default Arduino IDE installation will store libraries at ~/Arduino/ibraries - if this directory doesn't exist, create it.

Installing DHT Sensor Library

To read from the DHT sensor using Arduino IDE, you need to install the DHT sensor library.

wget -O DHT_sensor.zip https://github.com/adafruit/DHT-sensor-library/archive/master.zip
unzip DHT_sensor.zip
mv DHT-sensor-library-master/ ~/Arduino/libraries/DHT_sensor

Install Adafruit Unified Sensor Driver Library

You also need to install the Adafruit Unified Sensor Driver library to work with the DHT sensor.

wget -O Adafruit_sensor.zip https://github.com/adafruit/Adafruit_Sensor/archive/master.zip
unzip Adafruit_sensor.zip
mv Adafruit_Sensor-master/ ~/Arduino/libraries/Adafruit_sensor

Installing ESPAsyncWebServer Library

Follow the next steps to install the ESPAsyncWebServer library:

wget -O ESPAsyncWebServer.zip https://github.com/me-no-dev/ESPAsyncWebServer/archive/master.zip
unzip ESPAsyncWebServer.zip
mv ESPAsyncWebServer-master/ ~/Arduino/libraries/ESPAsyncWebServer

Installing Async TCP Library

The ESPAsyncWebServer library requires the AsyncTCP library to work. Follow the next steps to install that library:

wget -O AsyncTCP.zip https://github.com/me-no-dev/AsyncTCP/archive/master.zip
unzip AsyncTCP.zip
mv AsyncTCP-master/ ~/Arduino/libraries/AsyncTCP