A method without root, that works even with new Android versions:

Prerequisites:

- Linux, Windows or Mac
- USB cable for your device
- Android Device


Instructions:

 1. Install your device driver for using adb. Everything you need will you find [here][1]
 2. Download adb executable for your OS. It is part of the Android SDK, but you might be able to find the adb executable individually.
 3. Connect your android device.
 3. [Enable the developer options][2].
 4. Enable USB debugging.
 5. Open a command promt (windows) or terminal (linux / mac). How to do it: On Windows: windows + r > enter "cmd" (without quotes) > click enter | On Linux: You don't know how to open a terminal? LOL | On Mac: Type `Terminal` into Spotlight and open it
 6. CD to the directory where the adb executable is located. On Windows: Go to the directory where you downloaded the adb executable, Shift+Right Click and select "Open Console" (or similar) | On Linux / Mac: Rightclick in the directory and select "Open Terminal here" (or simply CD into the directory) 
 7. Type in your cmd/terminal: `adb devices` to verify your device is properly connected.
 8. If your device is properly selected, type in `adb logcat` to show the mighty and magic logcat aka stacktrace.
 9. Reproduce your error (or whatever) on your device.
 10. Right after, paste the whole cmd / terminal window into a paste-service like http://pastebin.com/ and send it to us.

*(Mostly copied from [Leandros](https://android.stackexchange.com/a/33217/501))*


 [1]: http://developer.android.com/tools/extras/oem-usb.html
 [2]: https://android.stackexchange.com/a/33497/501