It is possible to "power" a laptop using solar power, but it will not be cheap and you will be at the mercy of the weather since overcast and cloudy days will significantly decrease the amount of solar energy that can reach the solar panel.
Here is video for the PowerAdd 40w solar charger which costs $200m. However, 40w may not be enough to charge the laptop's battery while you are using it because as stated before, clouds can cause actual power to fluctuate. A better solution is probably the 60w version which sells for $320. Why is it so expensive? Well, it is portable and includes a voltage regulator. Alablcho provided a link to a solar panel, but you still need to purchase a voltage regulator to make it usable, otherwise you are talking about serious damage to electronics due to fluctuation voltage and amperage.
Get the power brick for your laptop, and see the details, it probably reads "65W, 19V". It will need twelve hours to fill in one KWh, which your utility sells you for like $.20, so we have the base - twenty cents for twelve hours (make it a day).
Now, you need a solar panel which can give 65watts on 19Volts. The closest match here is little bit over $100.
So, your investment of $100 will get break even after five hundred days - each of them with 12 hours of sun. Go figure whether it is worth.
Don't take me wrong - I am all about renewable energy. But in order to make a saving, you need an investment of several thousand dollars, not one Benjamin.