Wiring Lilypad USB + ESP8266 Serial WiFi Module
First, upload the sketch below to your Arduino. Then, try to tie RX (pin 3) and TX (pin 2) of SoftwareSerial together. Open the Serial Monitor and send some text and see if you get it back as a response.

#include &lt;SoftwareSerial.h&gt;
SoftwareSerial Serial1(3, 2);

void setup()
  {  Serial.begin(9600);
     Serial1.begin(9600);
  }

void loop()
  {
     if (Serial1.available())
         { char c = Serial1.read() ;
           Serial.print(c);
         }
     if (Serial.available())
         {  char c = Serial.read();
            Serial1.print(c);
         }
   }


Once you get a response, then your SoftwareSerial part is working and you can then try to connect to your ESP8266.