Just saw your reply now sorry.

No need to store the power in a minimalist solar setup - your laptop already has a battery!

Now the voltage out of the solar panel varies a lot - the intensity of the sunlight, the temperature, and how much power you're using all affect it. This is a nuisance for most purposes, but laptop chargers designed for cars are designed to take it :)

Yes, buying the "12 volt" panel is the first step and the most expensive. Look up your laptop and find out how many watts it uses. Make sure your panel can produce more than that. Some 12 volt panels end in bare wires, these are easiest for this use.

Then you need an adaptor for the output of the panel, usually clips at one end and a car "cigarette lighter" socket at the other, these are about $2 .

Then the laptop charger. Designed for 12v, but I've used these on systems running at up to 24 volts with no trouble.

This system only works during daytime, of course, but it means you can run your laptop during the day even when the power is out.

Hope this helps you!