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Beginner's guide to ESP8266 and tweeting using ESP8266
I'd like to help. Make sure you know the difference between the Baud rate that your Arduino uses and the Baud rate that the ESP module uses.. I used an UNO, and it's baud rate is 9600, so your serial monitor should be set up to that rate if using an UNO. Now, after the "AT+UART_DEF=9600,8,1,0,0" command, you need to alter the sketch you have loaded into the arduino, specifically the part that tells the arduino at the speed you are trying to communicate at.. for me, I had to go from 115200, to 9600 after the command.. after that, all my commands come back free of garbage. I hope this helps, I am a newbie to this and was stuck on something similar for quite a while!
Get Started With ESP8266 Using "AT Commands" Via Arduino
Remote Wi-Fi DHT11 Temperature and Humidity I2C 2 X 16 LCD Display With Two ESP8266 and Visuino