Solar powered charger for laptop
A. You will need to calculate your Energy consumption estimations. Let say, for 5 hours a day of average laptop consumption (70W) you will need to produce 450-550w a day (that is 350w plus energy losses on conversion of voltage and losses of battery). 

B. For this You will need:
1. Some kind of solar panels 
2. A solar charger
3. A battery 
4. An inverter

The specification of those element is depend on the strategy that you're planning to apply.

C. There are two basic strategies for planing this system:


You can use a 24V system and then get a DC-DC inverter (24v to 19v), OR you can use...
Mine preferred way, because the computer is a gentle electronic device, is to go through the transformer of the computer it self (that is, 220/110v AC to 19DC), as you can count on it to be accurate and stable for the computer and the internal battery system: use a 24/12v system with a inverter to normal appliance voltage in your region (220/110v) and plug the original transformer of the computer to the inverter.


You've a lot more to learn before i would recommend you to start spending money on materials.

You can read more here (cost 20$) - and I'm not getting paid for this. i don't even know the writer... i really do recommend this e-book, i have used it myself.
and here you can find an full and detailed article i wrote about how to build a solar pv electric system, but it in Hebrew, so maybe try to Google-translate it.

And here two more good pieces of content, from "Instructables":


http://www.instructables.com/id/DIY-Solar-Setup/
http://www.instructables.com/id/DIY-Home-Solar-Planning-a-Solar-Array-Beginners/


Hope you'll find this answer useful.