The lights go out.
That'll be the first thing that you notice. You'll look outside and will probably notice that the lights at your neighbours and the streetlamps are out too. Odd though, there isn't a thunderstorm, must have been some grid problem again, you'll think. You're used to power outages though, you've remembered to keep a flashlight handy.
But why won't your cell phone turn back on? That's bizarre. You'll also find that your car probably won't work either. While you don't know it now, its because the on-board computer systems are fried.
Now you may start to panic. Maybe it will cross your mind that you've just experienced an EMP attack, but maybe not. As night falls, and the lights have not yet come back on you'll be wondering how long before the electricity comes back. The answer may surprise you.
Months to years.
In 1999, during a tense moment in Russian-US discussions over NATO actions in the former Yugoslavia, a Russian Duma member declared that "if Russia wanted to harm the US without incurring nuclear retaliation, it would simply launch a single nuclear-tipped missile from a submarine and detonate it high in the atmosphere over the American continent... pulses of electromagnetic energy ... would wipe out the electricity generating and transmission system across a huge portion of the continent." 
The damage could take years to repair.
The Americans are well aware of the potential repercussions of such a strike. In 1962, a nuclear test code-named Starfish Prime detonated a 1.4 megaton nuclear warhead 400 km above the Johnston Atoll, causing electrical disruptions 1400km away in Hawaii.  To put it in perspective though, North Korea's latest nuclear test was only between 10 and 20 kilotons.
An EMP strike is a very real possibility and one that is being considered by many nations in the world, both how to commit an attack, and how to defend against one. Its hard to imagine a world without electricity for months but its been the fodder for science fiction works for years. While such an attack would produce no immediate casualties, its hard to imagine that it would not produce a nuclear retaliation, if that were still possible. MAD by another name I suppose.
 Kramer, D. "US electricity grid still vulnerable to electromagnetic pulses" Physics Today, September 2009.
 Day, C. "Very low-frequency radio waves drain Earth's inner radiation belt of satellite-killing electrons" Physics Today, August 2008