A couple years ago, my husband built a pizza oven, a giant fire-breathing, bug-eyed goldfish named Bubba, but for the most part, I've been left in charge of building the fire. Perhaps it's because I survived a long, cold Tennessee winter with only a wood burning stove? However, I discovered that building a fire inside a pizza oven was a bit different than building in a fireplace because the fire in a pizza oven requires a fair amount more finesse.
One thing that carried over from building in a fireplace to the pizza oven was my desire to make BIG FIRE! When I build the pizza oven fire, I try to get it so hot that the infrared can't measure the heat. Cos that's just how I roll. Also, after the fire is done erupting, the heat drops very quickly, but then the rate of decrease slows. If I take it to 1000F (538C), it'll drop to 800F (427C) in 45 minutes and then to 600F (316C) in 2 hours. Strangely, my husband doesn't let me build the fire unless he needs 800F+ (427C+) temperatures. I just can't do them small. :(
While this Instructable is about pizza ovens, most of these recommendations spill over into building a fire in a stove, fireplace, or bonfire. If you can perfect the pizza oven fire, you've got other fires nailed.
Garden hoe with wood handle
Bucket of water to put out the wood handle when it catches fire
Leather work gloves to prevent spider bites and molten plastic on flesh and to do most of the handling
Long oven mitts for the in-depth fire handling
Long metal tube for blowing in extra air and scattering ash
Sources for Cheap/Free Material:
Mailbox. Chances are you have newspapers, flyers, and brown paper packing material in addition to brown cardboard boxes. This is only good for starting the fire, but it's nice to have a solid stash of your favorite fire starting material. I've also chopped up old phone books because the inside pages burn quite nicely for the very, very bottom layer.
Your yard. Limb up your trees, collect fallen branches, cut down a declining/dead tree, or call a tree service to cut one down and leave the debris and trunks.
Bulk brush pick-up day. Here in Austin there are pick-up days for bulk brush which usually means branches and trunks that have already been cut down to an acceptable size. Stock up.
Weekly brush pick-up day. This isn't as good as the bulk pick-up because it's largely smaller yard waste like leaves, but occasionally there are a few good branches by the curb.
Craigslist. Some people will have downed trees that just need to be cut up, and these are usually listed in the "free" section.
Roadside stands. The best prices I can find when it comes to buying logs is along the roadside. Unfortunately, most of these you have to just stumble upon, and you cannot rely on someone being there when you need them.
Start your firewood stockpile as soon as you start building your pizza oven. Actually, start the stockpile 3+ months before you build your pizza oven for the sake of seasoning (i.e., making it less "green" by letting it sit for a season).
Use more kindling and paper than you think is necessary. It's hard to rebuild if there wasn't enough kindling to begin with. I also like to leave a bit of paper from the very bottom of the stack reaching towards the oven opening for easy lighting.
Build an evenly distributed platform with the kindling by using a mixture of branches and twigs from short to long. This will help maintain good air flow.
Always place the fastest burning material at the bottom and the the slowest burning material at the top. Example: Paper -> Cardboard -> Twigs -> Branches -> Small logs -> Larger logs.
Resist the urge to push the pyre over until you're ready to start baking. The longer you leave it standing, the more heat will be retained. Of course, if you got it too hot, rake the coals across the bottom the disperse the heat.
If you want it crazy hot, place logs vertically between the stack and the oven opening.
Build the logs up to the top of the oven. I like to create, essentially, a wall that separates the opening from the majority of the oven.
Use logs and split wood that are approximately 4" (10cm) in diameter and 18" (46cm) long for the bulk of the wood. I also like to throw one large log on top for longer lasting heat.
Once it gets hot enough, it doesn't really matter what sort of wood you use - it's going to burn FAST, but it's best to avoid resinous (e.g., cedar) or soft woods (e.g., crape myrtle) at least towards the very bottom of the stack.
When stacking, leave gaps between each log for air flow.
If you've just started your firewood stockpile, chances are that you've got some green wood. The day after firing the pizza oven when temperatures inside are 200F-250F (93C-121C), throw some of that green wood in the oven to kiln. It likely won't be dry by you're next firing, after all you're going to want to use that thing constantly because it's awesome, but it'll be better than nothing.
Signs You Did It Right:
The fire took using only a single match.
Smoke disappears within 5-10 minutes, and the fire burns "clean".
Bottom layer burns evenly before the fire reaches each upper layer and so on.
All the soot burns off inside the oven.
There's very little ash (compared to how much wood was burned) the next day.
Your face melts within 4' (1.2m) of the opening.
Have fun, tell your mother that you love her, and don't be stupid!