ESP8266 and the Arduino IDE

Part 1: ESP8266 and the Arduino IDE Using the Esp8266 with the Arduino IDE (Updated)
Part 2: Control an LED from a web page using Access Point Mode (AP)
Part 3: Control an LED from a web page using Station Mode (ST)
Part 4: Connecting to an ESP8266 with unknown IP address using mDNS
Part 5: adding wifiManager
Part 6: JavaScript and AJAX
Part 7: More Controls. 3 LEDs
Part 8: Auto Updating Webpage
Part 9: first steps with Websockets
Part 10a: IOT Website. Temperature and Humidity Monitor
Part 10b: IOT Website. Enhancing the Website
Part 10c: IOT Website. IOT Monitor Station. Add a LCD
Part 10d: IOT Monitor, the final project

ESP8266-01 Programming Breakout Board. Includes 3.3 voltage regulator for power, voltage divider for RX and switches for reset and programming.
Basic connection guide.
ESP8266 + serial adaptor
Arduino to ESP8266 By Serial Communication
Arduino & ESP8266 Webserver. An old example of a webserver using AT commands, can be done but very clunky and slow. Much better to now use the Arduino IDE. Useful if you want to know what is happening behind the scenes when using a library