How to connect an Arduino to the ADXL345 board

we have a breakout board.

What breakout board do you have?

to be frank,we don't understand the Figure 8 on the datasheet,especially the ALT ADDRESS

If you want to have two of the same deice on the I2C bus they need to have different addresses.

  Wire.beginTransmission(ADXAddress); // transmit to device 
  Wire.write(Register_X0);
  Wire.write(Register_X1);   ///// You can't request more than one register at a time
  Wire.endTransmission(); 
  Wire.requestFrom(ADXAddress,2);  
 if(Wire.available()<=2)       ///// If Wire.avaialble() < 2 you can't then read two bytes
  { 
    X0 = Wire.read();
    X1 = Wire.read();  
    X1=X1<<8;
    X_out=X0+X1;    
  }

Try something like this instead:

  Wire.beginTransmission(ADXAddress); // transmit to device 
  Wire.write(Register_X0);
  Wire.endTransmission(); 
  Wire.requestFrom(ADXAddress,1);  
 if(Wire.available())
  { 
    X0 = Wire.read();
    Wire.beginTransmission(ADXAddress); // transmit to device 
    Wire.write(Register_X1);
    Wire.endTransmission(); 
    Wire.requestFrom(ADXAddress,1); 
    if (Wire.available())
        {
        X1 = Wire.read();  
        X_out=X0+X1<<8;    
        }
    }