My favorite way to start a fire indoors and out is a method called the top-down burn. The interesting thing about this method of starting a fire is that it is the exact opposite of what most people do!
To start, put the very largest pieces of wood front to back on the very bottom. The next layer up, use slightly smaller pieces of wood but stack them side to side on top of the largest bottom wood.
Continue this process until the firewood has reached fifty percent of the height of the fireplace, and make sure each layer is progressively smaller and switching one layer front to back, one layer side to side.
Once you are at the top, this is where you will only have very small wood pieces (as small as shavings) that can be very easily started with little or no effort. The fire will start burning from the top and as it gets progressively larger, will ignite the larger logs below.
This method not only works great and keeps burning for a long period of time, but also produces less smoke than other methods of starting a fire.
I personally love using this method on a campfire. Instead of constantly feeding the fire every few hours, you can set up your campfire once and have it burn all night.
As with all methods of starting a fire, it is key to use moderation and do not ever use anything such as gasoline or other highly flammable substances to get a fire going.