What is required to connect solar panels to my home without connecting to the grid?
Typical grid connected installs of solar panels on homes need a couple of items to get them to work (it's not just lets slap some panels up there and wire it into the house).  Solar panels are DC (direct current), your house is AC (alternating current), so a inverter is needed to create the AC current.  Also that AC current needs to be synced to the same wave form that is being feed from the grid, another device (or sometimes packaged in the inverter).  Then the new solar AC is then tied into your main panel, typically requiring another box.  Also depending on the install, the panels might be electrically separated from each other (a good thing) requiring another device.  Once connected, excess power from the panels will feed back into the grid and in some areas this will be credited back to you on your bill.  

All said, this work needs to be done with a permit, typically with buy off from the power company on size of panels.  Also for most DIY'ers, this is out of their scope of skill.  Get some quotes from solar panel companies and electricians in your area to get an idea of what you are looking at.

Also look at the cost of the system and how much it is going to save you each month.  Solar is popular here because power goes up to .30 a kWh depending on usage.  But for my energy usage, I'm only sitting at .11 on average making solar unreasonable.  My last bill was under $2 after energy program usage credits where applied.