The Android logging subsystem uses different log buffers: events, main, radio and system.
Generally speaking, when the issue you encountered concerned telephony, including data (3G), the buffer you want is radio. In any other case, that's the main buffer you want.
There are various ways to obtain logs:
Instructions to install ADB: ToolsInstallation
Now use adb this way:
adb logcat -b [BUFFER]
aLogcat is a (free) Android app that will collect logs and save them to a file, either regularly or when you press the Save button from the app menu.
You can set the desired buffer from the Preferences.
After saving the log, you can get it from a file stored in the alogcat folder on the root of storage.