Step one:  Go to Wal-Mart and purchase a 12 volt deep cycle trolling battery for around $39 (plus a $5 recycle fee if you don't turn an old battery).  It will probably have a 75 amp hour capacity depending on brand.  Also get a $6 plastic battery box to put it in.  While you are in the auto section check on their inverters.  You can pick up a 350 watt one for $39 (or a smaller 175 watt one for $29).

Step two:  Go to your local Harbor Freight store to purchase your solar panel.  They range from $10 to $300.  Roughly $50 will get you 5 watts, $150 will get you 15 watts, $300 will get you 45 watts.  Depending on your usage and budget, select one.  Lets assume you go with a 5 watt one.

Step three:  WIRE IT UP!  Your battery has a (+) and a (-) terminal.  Your inverter has the same on it's cable.  So does your solar panel.  If you are lucky, the panel & inverter have clips that just clip on the battery terminals.  If not, just skin the wires and tighten them up under the wing nuts on the battery terminals remembering to keep the (+)'s together and the (-)'s together.  Just use the wires that come with them and do not extend them. 

Step four:  NOW IT'S MATH TIME!!!   If your 12 volt battery is 75 amp/hours, how many watt/hours is it?   answer... 12 x 75 = 900.  That means it will run 900 watts for one hour or one watt for 900 hours.
If your laptop is 25 watts then how long will the battery last? 
answer... 900 / 25 = 36.  Theoretically it will run 36 hours but it will be less due to losses.
So do the math on your TV, fan, or whatever you want to run and see how long it will last on your battery.  (This is why I have 16 on my house system!)

Step five:  We have to charge that battery back up so it's MATH TIME AGAIN!!!  (You should have done your homework in school so this would be easy...  hopefully I'm making it easy)  Question - How long will it take your solar panel you bought in step two to charge your battery back up?  answer... depends on how much you used it!  If you used your laptop for one hour than it will take one day.  5watts x 5 hours of sun a day (average) = 25watt hours per day.  If you want to use your laptop two hours a day and be fully charged up, you better buy the 10 watt panel. Three hours - three panels, or one panel charging three days. 

This way you have completely gone off grid with your computer (or whatever) for around $139., you also have an emergency backup power supply for whatever,  and you have actually gone solar on a small scale.  Who knows, maybe next you'll add on to this system and have 4 batteries and 4 solar panels.  It all works the same!