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;
}
}