That you want to use an ESP8266 module probably means you want to do it over WiFi, this as there are also ethernet shields for the Arduino.
There are lots of tutorials out there of how to send data to a web site, it all depends on what you want. The ESP can act as web server (and host complete web sites) by itself, it can connect to a remote server and post information over MQTT, as http POST, or connect to a MySQL server, and there are probably more options. It's up to you what you want to do.