1) Unzip mineways.zip, the whole thing, to some directory. Don't try to run it from inside the zip file!
2) Double-click the Mineways program to run. Use "File | Open World" to select a world.
3) Use the left mouse button to drag the map around, use the mousewheel to zoom.
4) Drag with the right mouse button to select an area on the map and to adjust this rectangle.
5) Optionally use the middle mouse button or "Lower depth" slider to select a depth.
6) Export the model for 3D printing by "File | Export for 3D Printing..." - just hit "OK" on the Options dialog.
Not clear? Watch this quick introduction or this longer tutorial to see what's what. You can find more tutorials on the video playlist.
Problems? See the Troubleshooting Guide.
Exporting creates a .zip file by default. To preview your model, unzip the .zip file (there is also a checkbox on export, "Create files themselves", to avoid unzipping) and open the .wrl file with MeshLab or other VRML file viewer. If you want to 3D print your 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.
What to try next: check out the "Export lesser blocks" feature, which lets you get more detail. This feature is not on by default because it has some risks - read up! To learn more about other options work through the documentation page, the information is pretty much in order of importance.
Super-fast quickstart for rendering: Same as for 3D printing export, but instead select "File | Export for Rendering..." - just hit "OK" on the Options dialog. You can preview the output OBJ file by using G3D, MeshLab, or any other OBJ file viewer. To import the model to a rendering program, see this area of the documentation.
Platform-Specific Stuff
For Windows 8, if mineways.exe doesn't work for you, try mineways_windows8.exe. If you are informed that msvcr120.dll is missing, you will need to install the 64-bit version of the Visual Studio 2013 redistributables in order to run it.
For Linux, download the Windows version and then use WINE to emulate Windows.
If Mineways is blocked by Norton Antivirus: 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.
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. 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.
When you try to export, if you're exporting a file with block textures applied you may be warned that the terrainExt.png file is not found. Use "File | Set Terrain File" and select the terrainExt.png in /users/<your name>/Downloads/MinewaysMac or wherever you put mineways.exe.
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.
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. Otherwise it's the same as the PC version, and Mac users can also use MeshLab or GLC Player for viewing exported 3D models. See the main documentation page for (way) more help.
We use WineBottler to make mineways32.exe into a Mac app - it's pretty easy! Here's a screenshot of the settings I use. Save to some directory as "Mineways," wait a while, and then you can run (and redistribute) the Mineways.app produced. Or not: currently I can't get WineBottler to make a new version of Mineways.