Downloading logs via the Terminal
If using ArduCopter 3.1.5 (or earlier) this is the only method for downloading logs. If using AC3.2 (or higher) this option is available only to Pixhawk users and may be useful for downloading large logs because it is faster than downloading via MAVLink. To download via the terminal:

  • Open the Mission Planner’s Terminal Screen
  • push Log Browse button and open the .log dataflash file

The Log Browser screen will appear with a graphing area at the top. This graphing area’s size can be changed by clicking and holding on the area just below the graph but above the green graphing buttons.
Downloading logs via MAVLink
This method is available in AC3.2 (or higher).

  • Connect your vehicle to the mission planner using the micro USB cable
  • Open the Mission Planner’s Flight Data screen
  • On the bottom left, select the “DataFlash Logs” tab and push the “Download DataFlash Log Via Mavlink” button

Then, select the log you want to download. This will save that log to your MissionPlanner/logs directory, in a folder named after the vehicle type, such as QUADCOPTER. 
More details here.
To learn how to read .Log data click here. If you are unsure about your reading or need help on the analysis try posting your log here (Plane .Log) or  here (Copter .Log).