Connecting Arduino to the ESP8266
Absolutely. I'll use the Arduino UNO and the ESP8266-01 WiFi module as an example:






The ESP8266 works with 3.3V and not 5V, so you need to connect the 3v3 pin on the Arduino to the VCC and CH_PD pins on the ESP8266.
Connect the GND pin on the Uno to the GND pin on the ESP.
Connect the RESET pin on the Uno to GND. Grounding the RESET pin
effectively causes your Arduino to work as a dumb USB to serial
connector (which is what we want to talk to the ESP8266).
Connect the CH_PD pin on the ESP8266 to the 3.3V line
Connect the RXD pin on the Arduino Uno to the RX pin of the ESP8266.
Connect the TXD pin on your Arduino Uno to the TX pin of the
ESP8266.


Normally, when you want two things to communicate over serial, you'd connect the TX pin of one to the RX of the other (send --> receive). In this case, however, the Arduino isn't talking to the ESP8266; the computer is talking to the ESP8266 via the Arduino.