Super-fast quickstart for 3D printing and rendering export:
1) Unzip mineways.zip, the whole thing, to some directory. On Windows you can actually run mineways.exe from the zip file.
2) Double-click the Mineways.exe program to run (try the Mineways32.exe if that fails). If things don't start up correctly, see this guide.
3) Use "File | Open World" to select a world.
4) Use the left mouse button to drag the map around, use the mousewheel to zoom. "F3" takes you to the player's location.
5) Drag with the right mouse button to select an area on the map and to adjust this rectangle.
6) Optionally click with the middle mouse button or set the "Lower depth" slider to select a depth.
7) Export the model for 3D printing by "File | Export for 3D Printing" - just hit "OK" on the Options dialog. For rendering, use "File | Export for Rendering"
8) Optional: if you want to see the result, view the .OBJ or .WRL with G3D, MeshLab, or other 3D model viewer (avoid 3D Builder if you use colors; it's fine for STLs).
Not clear? Read over the quick reference page or watch this quick introduction or this longer tutorial to see what's what. For using a home or school 3D printer, see this more in-depth guide at MinecraftEdu. You can find more tutorials on the video playlist.
Problems? Look below for platform-specific problems, then see the Troubleshooting Guide.
3D Printing: To preview your exported model to see if it's what you want, open the .wrl/.obj/.stl file with MeshLab or other model viewer. If you want to 3D print your model and don't have a 3D printer (or want a multicolored model), create a free Shapeways account and upload the .zip file. Once the model is processed by Shapeways (a few minutes), you can order it - make sure to select "colored sandstone" for the material.
As an example, here's my non-profit store. Note that no part of this process will cost you anything, unless you actually order something. Sculpteo is another 3D print service worth considering (see my sample store). It's generally more expensive but often delivers more rapidly (even shipping from France!). There are other 3D print services such as 3D Hubs; see a list here.
Rendering: see this section for how to import your model into various rendering and animation systems.
What to try next: work through the documentation page to learn more about other export options. The information is pretty much in order of importance. In particular, for 3D printing, check out the "Export lesser blocks" option, which lets you get more detail. This feature is not on by default because it has some risks, so read about them there.
Platform-Specific Stuff
Windows
If Mineways gives you an error on startup on a Windows PC, try Mineways32. If you get an error about MSVCR130.DLL being missing, you'll need to install the Microsoft Visual C++ 2013 Redistributable Package for your system. Select vcredist_x64.exe for your 64-bit system, vcredist_x86.exe if your system is 32 bits. To find out if your computer is running a 32-bit or 64-bit version of Windows, follow the instructions here, which come down to "hold down the Windows key and then click the Pause|Break key, then look for System type". Mineways32.exe should run on any PC, but export size is somewhat limited (this usually doesn't matter for 3D printing); Mineways.exe is 64-bit and will run on only 64-bit systems.
For Windows 10, there is a Windows 10 Edition Beta of Minecraft. This is essentially the Pocket Edition, which Mineways does not currently understand. You need to use the normal PC or Mac version of Minecraft to use Mineways.
If Mineways is blocked by Norton Antivirus, e.g., you get an error that Windows is not being able to "access the specified device, path or file": First, make sure you are downloading Mineways from this site, i.e., the links above. If the download is being autodeleted, here's how to turn Norton off temporarily. Otherwise, just run Mineways and ignore the warnings. No other antivirus software reports Mineways as having a virus, so I believe it's a flaw in Norton. I won't be insulted if you are cautious and don't follow my advice, but Mineways is open source, and I have a reputation as a good person, so these things count against there being a virus. You can also try running older versions of Mineways, this has been known to work.
Linux
For Linux, download the Windows version and then use WINE to emulate Windows. Note: this also works on the Mac; the Mac version is merely the Windows version plus the WINE executables wrapped around it.Mac users:
Download Mineways for Mac.
Once installed, run Mineways - it'll take awhile to start the first time and you'll get a notice about Wine, so be patient. To load your world, use "File | Open World". If none of your worlds are listed, you'll get a warning and will need to use "File | Open..." and navigate to /users/<your name>/Library/Application Support/minecraft/saves/<your world's name> and select the level.dat file there.
By default, Mineways now uses its own tile textures that are stored in the program itself. Other "terrainExt.png" can be used - a number of these come with the program. Use "File | Set Terrain File" and select the terrainExt.png in /users/<your name>/Downloads/MinewaysMac or wherever you put Mineways. You might need to search for these files, just use Spotlight and search on "terrainExt.png". The other terrainExt*.png files will be found in this directory.
When you save, go to the directory /Users/<your name>/Documents to save. The Mac version is only 32 bits, so cannot export very large areas that the PC version can. This normally doesn't matter for 3D printing, since you want to keep the models small. If you do find you're out of memory, try the "Give more export memory!" option under Help, which clears out the map cache before trying to export the area you've selected.
Otherwise the Mac version is the same as the PC version, and Mac users can similarly use MeshLab or GLC Player for viewing exported 3D models. See the main documentation page for (way) more help.
Troubleshooting for the Mac
If you get the warning "'Mineways' can't be opened because the identity of the developer cannot be confirmed." take steps similar to those explained here. The short version: right-click and select "Open," then verify that you want to run the program. Yes, I'm trustworthy.If you get the message "Couldn't find your Minecraft world saves directory..." you'll need to guide Mineways to wherever your world files are saved on your computer. Follow these instructions. If you are using a Mac with a language that is not English, Mineways may still have problems with the path to your files. One solution is to copy your world files to a USB flash drive - this avoids the path problems. Another solution may be to temporarily change the language to English.
If you can't see the Application Support/minecraft folder, see this page for how to use the terminal utility to make it visible. Short version: search for "terminal" in spotlight, copy and paste this line into the terminal and hit Enter:
defaults write com.apple.Finder AppleShowAllFiles TRUE
Then type or paste this line:
killall Finder
to restart the finder. You can find your saves folder by opening Finder -> Go -> Go To Folder -> type ~/Library/Application Support/minecraft/saves. For future reference, it's best to make an alias for this folder and copy it to your desktop.
Selection is done with right-click; if you are using a trackpad or your mouse cannot right-click, hold down the Control key and left-click, or see this page for more options.
We use WineBottler to make mineways32.exe into a Mac app - it's pretty easy! Start it up and click on "Advanced", the rightmost icon at the top of the application. Here's a screenshot of the settings I use; I've renamed mineways32.exe to be Mineways.exe for this example. Click "Install", save to the "Documents" directory, and "Save As: Mineways". Wait a while, and then you can run (and redistribute) the Mineways.app produced. Note: do not save to the original Mineways directory where the mineways32.exe file is located, as this will cause a loop and the program will never finish.