How to connect an Arduino to WIFI using an ESP8266
Sending the following commands to the ESP should get you started:
AT+RST # Reset
AT+CWMODE=1 # Set to station-mode as a client
ATE0 # turn off command echo
AT+CWLAP # optional: list access points
AT+CWJAP_DEF="SSID","PASSWORD" # Always connect to this SSID
(I made-up the comment syntax; don't try to send those.) The full ESP8266 AT Instruction Set has the complete set of commands and a functional description of each one.
Update:
... do I need to connect RX of ESP8266 to RX of Arduino, TX of ESP8266 to TX of Arduino, Ground of Arduino to RESET ?
Rx & Tx must be cross-connected with the corresponding Arduino pins and the ESP's reset pulled high (3.3v).