Short video instructions:
Instruction for the Joy-IT ESP-01 module (German):
The official GitHub repository for ESP8266 with Arduino IDE: https://github.com/esp8266/Arduino. It also provides howtos for different types of installation. I prefer the Board Manager method. Enter
http://arduino.esp8266.com/stable/package_esp8266com_index.json
into Additional Board Manager URLs field. You can add multiple URLs, separating them with commas.