Thought I would jump in while you are waiting for Peru (Bob) to respond.
Extracting a portion of a clip is relatively easy using Premiere Pro CS6. First, you'll want a sequence that matches the properties of the footage. The easiest way to do that is to import the footage and drag the clip in the project bin and drop it on the "New Item" icon at the lower right of the same bin. That will create a new sequence matching the clip properties and automatically add the clip to the sequence. Or, you could create a sequence and drag and drop the clip to the sequence -- Premiere Pro CS6 works like Premiere Elements in that it will offer to change the sequence properties to match the first clip added.
There are numerous ways to select the portion to extract. You could display the clip in the source monitor, set the in/out points and drag the segment from the source monitor to the "new item" icon or to an existing sequence. You could set the in/out points of the sequence. You could set the work area bar. You could edit the clip and cut out unwanted portions. Or, you can even set the in/out points in the export dialog. Pick one.
However you do it, select the sequence you want to export and invoke the export dialog (shortcut ctrl+m). In the Export Settings section, select the "Match Sequence Settings" checkbox. Do not check the boxes at the bottom of the dialog. Click on the Export button if you want to export immediately using Premiere Pro CS6 or the Queue button if you want to continue working in Premiere Pro and let Adobe Media Encoder do the export in parallel.
GoPro uses h.264 which is not a lossless codec so you will get some compression loss. But, it should be able to hold up well enough that you would be hard pressed to see a difference for a couple of generations. I wouldn't worry excessively about it. You could export using an intermediate/lossless codec such as Lagarith, but then the person you gave the exported clip to would need to have that installed on their system too.
Cineform is also an excellent codec to use as an intermediate. Premiere Pro CC 2014 actually has it natively included. It's not completely lossless, but the quality will hold up over many generations. Premiere Pro CS6 doesn't include Cineform. Cineform is included in the free version of GoPro Studio. I haven't tried installing that to see if Premiere Pro CS6 will be able to recognize and use Cineform. If you do try, keep in mind that the implementation of the Cineform codec will write to a .mov file on Windows and Mac, so you will need to select Quicktime and then Cineform (if it shows up).