Also please note that while you can use the ESP8266 as a "peripheral" to Arduino, to send AT commands, it is a pretty primitive way of doing things and I don't think it's much recommended anymore, except in very special cases.
The chip inside the ESP8266 is already much more powerful than any Arduino, so why not use that, and cut out the middleman, so to speak? There are many excellent libraries available for all sorts of Web stuff. You can program the ESP8266 from the Arduino IDE, as I already said, so that side of things should be familiar to you.
If there is already some major Arduino project the you have invested in, then there are probably still better ways to connect to the ESP8266, other than AT. (UART, I2C, SPI, etc). Most small Arduino projects though are easily re-implemented on an ESP8266, usually to advantage.
If you insist on using the AT commands, perhaps as a learning experience, OK. It really is not the best way, though. Also if you have somehow flashed something else over your chip, you will have to reflash the original factory firmware if you want this to work. I think you probably haven't, as you'd have seen the blue light flashing if you did... but even so, no big deal.