1. Install the Android platform tools.
Windows: https://dl.google.com/android/repository/platform-tools-latest-windows.zip
Mac: https://dl.google.com/android/repository/platform-tools-latest-darwin.zip
Linux: https://dl.google.com/android/repository/platform-tools-latest-linux.zip
2. Unzip the archive in some directory, for example, C:\adb (example for Windows).
3. Open the command line (for Windows, type Windows key + R) and cd to the adb directory.
4. Make sure the command adb runs from the command line.
5. Install the adb (Android Debug Bridge) drivers: https://adb.clockworkmod.com/
6. Unlock the Developer options on the device. Open Settings - System - About phone, find the "Build number" field, and tap 7 times on it. You must get a message "Developer mode unlocked". More detailed info can be found here.
7. Open Settings - System - Developer options, and set the "Enable USB debugging" flag.
8. Connect the device to the computer by USB cable. You must get a popup "Allow USB debugging?". Allow USB debugging.
9. Run the command "adb devices". The command should output the device ID.
10. Run the command "adb logcat > logcat.log". This command will write the Android log to a file (wait 20-30 seconds to complete the output). Then click Ctrl-C to stop running the command. The file logcat.log will contain the desired data.
Notice: Steps 1-5 may be replaced by installing Android Studio. However you may need to find the adb executable and add the path to this file to the "PATH" variable. For Windows, the path would be: %LOCALAPPDATA%\Android\Sdk\platform-tools