While iron isn't very rare, it is needed for a lot, especially if you want to build a structure out of it, build long railways or something like that.
What should you do to find/get a lot of iron with non-excessive effort (an inital effort for a good long-term solution is good though)?
Some tips:
The "mathematical analysis" is seriously flawed, because you're not looking to get every single ore in the block. Instead, you want to get as much ore as possible per second. This means that you need to see as many "fresh blocks" as possible per second. Let's look at one statement made in the analysis:
Not bad. With every 2 blocks destroyed (or 8 seen), we get 3.7% iron. Halve that to get the value of one block, which is 1.83% iron per block. That means for every 54 blocks of stone we mine, we'll get 1 iron ore.
Except, whenever you add a turn to your mineshaft, your digging causes you to see the other faces of the same two blocks you just saw. So don't add turns - which is exactly what a branch mine does every 4 blocks. Furthermore, when you do find ore in your branch mine, you'll dig towards your other shaft, and this will let you see some blocks that... you already saw when you dug that other branch. If you're going to shaft mine, make it one long shaft at level 14.
So what about caves? How many "fresh blocks" do you see per second in a cave? Well... a lot. To get an estimate, I started a fresh game on normal, punched a couple trees, a couple stone picks, bunch of sticks, a sword. Found a decent cave system. Coal pretty quick, sticks became a bunch of torches, I hear groaning. Strategy? Run like a boss, place torches, look at ceilings, floors, nooks. Don't stand still. Found iron? Great: spot check for monsters, then mine it. It does spawn diagonally. Check anyway. Hit dead end? Go back, seal the cave shaft up with a horizontal line of cobble, so you don't go in again. I got 54 iron in 10 minutes of caving. And a lapis block. The guide says (I wouldn't trust the math) that I'll get that much in 21 minutes using branch mines. Caves are better. Also, cave mining is much more fun.
TL;DR: Go a ways SW of spawn (fixed as of Beta 1.6), find a cave system, go deeper than sea level. Run through it placing torches.
Iron, fortunately, spawns close to sea-level. This means that an easy way (if a little time consuming) is to simply walk around the overworld until you find a cave entrance, and then explore that cave, you'll find, if you're lucky a vein of iron or two (don't forget to mine out all the blocks adjacent to any iron you find - 'veins' of iron can sometimes connect diagonally).
This gets you maximum iron with minimal digging, assuming that it is faster to explore a cave / walk to the next one than to mine blindly through the earth.
The other option is using an external minecraft utility, either to directly edit iron (or iron ores) into your inventory, or using something like minecraft xray to find the closest veins of iron (after which, you can dig directly towards).
Iron Golem Farm. The initial effort is immense but then the idea is quite fun on and by itself. Although the initial investment in railway to deliver necessary villagers may be rather... excessive; while the whole farm requires 13 iron total (a bucket and two hoppers) the most surefire way of delivering villagers is by rail, and that can quickly become quite costly.
Anyway, look up some tutorials on making an iron golem farm. Find a village. Gather lots and lots of cobblestone, quite a bit of wood, have a little lava handy, make an infinite water source at the site so that you don't have to run for miles...
Then busy yourself with building something near your farm and find a new stack of iron every hour or two deposited in the collection chest.
I like to play the Hunger Games a lot on Minecraft and so it's very important to be able to find Iron Ore very qucikly and as much as possible. My personal opinion is to find a spot, somewhere you just like or maybe just a random place, then dig straight down. I go to the Bedrock and then from there dig steps toward the surface, randomly digging out little rooms when I feel I might get lucky. If I do happen to find Iron, I dig around that area to make certain I have collected it all. But be very careful of water, lava, and monsters finding you. Good luck :)
There are several ways to find iron. Many people use methods of branch mining in natural caverns or cave systems found when digging straight into the ground (that is if you are lucky.) Beginners have a good shot to find several pieces of iron ore when exploring caves (they lie on the side walls.) Since iron is found around sea level it would be a good idea to dig in sandbars that are closer to lakes. Don't get discouraged if you find a lot of dirt, this will quickly shift into stone, coal, iron, etc. the more you dig. If you are a bit more experienced, you can give a shot on digging a set of stairs that leads approximately 14-20 blocks deep. Branch mining allows a player to cover a large amount of space and stumble across several veins of iron/coal. In Minecraft, that deeper down you go, the rarer the resources. However, it isn't the best of methods because of the waste of area, as well as the risks of lava flow, monsters, and sudden falls. Stack up on many pickaxes and torches, and don't forget, enjoy the game, don't make it a job.
You want my advice? Tackle those "annoying" gravel veins! I personally jump for joy whenever I find a vein of gravel, because I know that you will find ores more often if you go through veins of gravel, and this includes iron.
I personally find lonesome veins of iron very rarely, but when I go after gravel veins, I can find about 2 veins of iron, and a sizable amount of coal in the process too! Of course, finding caves is a good method too, but they carve away the rock, which includes the iron ore. Thus, you can find many veins of iron in a cave (and I'm not discounting the fact that it's a good idea) but they tend to be fairly small.
Go after gravel, it tends to yield more coal and iron. If you're searching for other types of ores, you're on your own, this trick only works with coal and iron.
This method occasionally is a bit fruitless, but it does yield good results when you find the ores. You can also try mining around the gravel vein a bit, just to make sure you don't miss anything.
Dig straight down under sand, you will find dirt and then iron.
I think it is most easy to look in caves that open to the surface. Another great method is looking around those gravel veins. You can find many ores when you do that. Even Diamond! But if you want lots of iron. It's a good idea to bring a pickax with the double wielding enchantment, which allows you to sometimes get double the item you are mining. :)
Scuba-Mining
One of the most common ways of finding Iron is to explore caves, primarily due to its efficiency. However, I found that Scuba-Mining presents a similar amount of efficiency and fun.
Step 1:
Find a sea are with the bottom made of stone. These can be quite rare in comparison to dirt, but I typically find these farther from the spawn point
Step 2:
Bring a pick, as well as a door. When at the bottom of the ocean, you can place the door and use the air blocks it creates to restore your breath. A more efficient form of Scuba-Mining requires a helmet enchanted with water breathing.
I typically focus on Scuba-Mining when I've exhausted nearby caves or I've created a base far from the spawn point. There have been many times that I've found few resources at the bottom of these oceans, but several successful mining runs have netted me multiple stacks of iron and coal.
I like to mine near lava; because it gives off light, I don't need torches. If you use Tab you should not fall into the lava. I just played singlemode and found over 30 iron ore in less than 30 minutes this way.
get near the bottom of the map and dig in a straight line until you hit dirt. Dig out all of the dirt that you can see with a shovel. It is faster than digging stone and yields better results. When the dirt is all dug keep going in a straight line and repeat. bring 1 diamond/1 iron/2 stone pickaxes and 1 diamond/2 iron/4 stone shovels.
