What's the fastest way to find mineshafts?

I'm on the hunt for melons, and one place I'm fairly sure I can find them is a mineshaft. Which leaves me back at square one, how do I find a mine shaft? It seems they were made substantially harder to find between 1.8 and 1.0.

What's the fastest way to find a mineshaft?

Abandoned Mineshafts are obvious once you've spotted them, since (with the exception of the libraries within Strongholds) they are the only naturally generated structures that use wood and fences. In addition, there are cobwebs scattered around them, especially around Cave Spider spawners.

There aren't any surefire ways of finding Abandoned Mineshafts, but you could start by exploring various caves, and once you see Wooden Planks, you know you've found one. The Minecraft Wiki page suggests looking for a ravine, since Abandoned Mineshafts are sometimes found intersecting them, and the wood structures will be a dead giveaway. They're not like Strongholds where you can use Eye of Enders to find them; you'll have to go spelunking if you want to find the mineshafts.

Abandoned Mine Shafts are not locatable by any special means, but they have the characteristic of significant horizontal extent. Find a ravine, then search its length. If a mine shaft intersects a ravine, the mine shaft will have wooden bridges crossing the ravine.

There must be a minimum and maximum depth (Y coordinate) at which mine shafts occur, so you could also limit your search to those levels, but I don't see that documented on the wiki.

I had the same problem (needed melons) and the same quesion (how do I find a mineshaft?) about a week ago. I spent about 3 days cave delving hoping to find one without any luck and started to browse through wikis. SUCCESS!! Apparently, for whatever reason, there is a near certainty of abandoned mineshafts being generated underneath desert biomes. Sure, they show up other places as well, but for some darn reason desert biomes almost always have one.

After finding this information I dug under the first desert biome I found, and sure enough found an Abandoned Mineshaft. Worked for me. Might work for you.

Source

Check the Exploration section.