Arduino ESP8266 S0 only.cpp

   #include <SoftwareSerial.h>
   #define SSID "enter the SSID"
   #define PASS "enter the password"
   #define DST_IP "220.181.111.85" //baidu.com
   SoftwareSerial dbgSerial(10, 11); // RX, TX
   void setup()
   {
     //setup RGB LED as indicator instead of softserial
     pinMode(3, OUTPUT);
     pinMode(4, OUTPUT);
     pinMode(5, OUTPUT);
     pinMode(6, OUTPUT);
     digitalWrite(3, HIGH);
     digitalWrite(4, HIGH);
     digitalWrite(5, HIGH);
     digitalWrite(6, HIGH);
     
     
     // Open serial communications and wait for port to open:
     Serial.begin(9600);
     Serial.setTimeout(5000);
     dbgSerial.begin(9600); //can't be faster than 19200 for softserial
     dbgSerial.println("ESP8266 Demo");
     //test if the module is ready
     Serial.println("AT+RST");
     delay(1000);
     if(Serial.find("ready"))
     {
       dbgSerial.println("Module is ready");
       //blink green 1sec
       digitalWrite(5, LOW);
       delay(1000);
       digitalWrite(5, HIGH);
      }
     else
     {
       dbgSerial.println("Module have no response.");
       //blink blue 1sec
       digitalWrite(3, LOW);
       delay(1000);
       digitalWrite(3, HIGH);
       while(1);
     }
     delay(1000);
     //connect to the wifi
     boolean connected=false;
     for(int i=0;i<5;i++)
     {
       if(connectWiFi())
       {
         connected = true;
       //blink blue 1sec
       digitalWrite(6, LOW);
       delay(1000);
       digitalWrite(6, HIGH);
         break;
       }
     }
     if (!connected){while(1);}
     delay(5000);
     //print the ip addr
     /*Serial.println("AT+CIFSR");
     dbgSerial.println("ip address:");
     while (Serial.available())
     dbgSerial.write(Serial.read());*/
     //set the single connection mode
     Serial.println("AT+CIPMUX=0");
   }
   void loop()
   {
     String cmd = "AT+CIPSTART=\"TCP\",\"";
     cmd += DST_IP;
     cmd += "\",80";
     Serial.println(cmd);
     dbgSerial.println(cmd);
     if(Serial.find("Error")) return;
     cmd = "GET / HTTP/1.0\r\n\r\n";
     Serial.print("AT+CIPSEND=");
     Serial.println(cmd.length());
     if(Serial.find(">"))
     {
       dbgSerial.print(">");
       }else
       {
         Serial.println("AT+CIPCLOSE");
         dbgSerial.println("connect timeout");
         delay(1000);
         return;
       }
       Serial.print(cmd);
       delay(2000);
       //Serial.find("+IPD");
       while (Serial.available())
       {
         char c = Serial.read();
         dbgSerial.write(c);
         if(c=='\r') dbgSerial.print('\n');
       }
       dbgSerial.println("====");
       delay(1000);
     }
     boolean connectWiFi()
     {
       Serial.println("AT+CWMODE=1");
       String cmd="AT+CWJAP=\"";
       cmd+=SSID;
       cmd+="\",\"";
       cmd+=PASS;
       cmd+="\"";
       dbgSerial.println(cmd);
       Serial.println(cmd);
       delay(2000);
       if(Serial.find("OK"))
       {
         dbgSerial.println("OK, Connected to WiFi.");
         return true;
         }else
         {
           dbgSerial.println("Can not connect to the WiFi.");
           return false;
         }
       }

Do you misspell some Serial vs dbgSerial.. check the line when you send a commnad.. Serial.println("AT+RST");

I agree with renexdev, I'm a newbie, this just made me more confused. I don't know how to fix it. Please review the code.

Wiring - RX from ESP to digital pin 10, same - TX to 11. Power supply from 5V step down to 3.3V
I think this schematic works - http://www.martyncurrey.com/wp-content/uploads/2015/01/Arduino-to-ESP8266.jpg
And yes it goes on AT+RST dbgSerial, not Serial

"if (!connected){while(1);}" maybe better put some code for reset and indicator reset, on this point arduino gets frozen and requests manual reset