Inevitably if you want to go solar, your going to need to do some research. While there are companies out there that would love to install a solar system for you, we're trying to save money here and they love to charge you over 400% in labor costs for something you can easily do yourself.
The best way to start is with an all inclusive kit, that way you get all the component you need to start out, and once you understand the basic simplicity of it all, you can expand.
If you shop around you can find some amazing deals, but in my ventures, Harbor Freight has the best one I could find for beginners. This wonderful kit, prices at $199.00 includes a 45 watt solar panel, a charge control module (so you don't blow up your battery), and 2 12v lights if your using it in a garage or shed, you can even install these in various rooms in your house, but that involves running wires, which we will discuss later.
the only thing it doesn't come with is a battery, but any deep cell battery will do, similar to the one in a heavy duty truck, or a boat, you can find these pretty cheap at auto salvage yards. For example, parts galore sells batteries out of salvaged vehicles for $10.00 a piece, so shop around, get a good deal. You could use a regular car battery, but they tend to wear out if you let them drop below a 50% charge rate on a regular basis. You'll also want a 300 watt inverter to switch from 12v to 120v, and you can pick one of these up on ebay for around 20 dollars. So, now how to set it up...
you'll want to put it where the panels receive the maximum amount of light during the day, as exposure to a good 8 hours will completely charge your battery, which in turn can provide enough power for a full 18-24 hours on a general load, such as lights, or a small appliance like a computer, tv, etc. later on, as you add panels and increase your battery bay, and pick up a larger inverter, etc you'll be able to power more things in your home, and eventually your entire home, becoming self sustaining.
The trick is to start small and simple, so you can understand what your needs are and how the system works, you can always expand later.