You should not count the number of pulses, but the number of transition from 0 to VCC volts or VCC to 0 volts (called rising resp. falling edge).

If you don't want to solder, you can also use a light dependent resistor (LDR) very close by the LED to measure the difference in brightness. See also chrisl's remark below.

The counting you can do manually (in a loop, check as often as possible or needed), or by setting up a timer to check for either rising or falling edges.

I will give the pseudo code so you can figure out the actual code:

    bool _ldrPin;
    unsigned long int _counter;


    setup()
    {
       // Set Serial
       Serial.begin(9600);

       // Set LDR
       setAnalogPin(X, INPUT);
       _ldrPin = readAnalog(X);
    }

    loop()
    {
        if (!_ldrPin && readAnalog(X) == HIGH)
        {
            // Rising edge, increase counter
            _counter++;
            Serial.Write(_counter);
            _ldrPin = true;
        }
        else if (ldrPin && readAnalog(X) == LOW)
        {
           // Falling edge, reset status
            _ldrPin = false;
        }
    }