I don't know much about photography and would be happy if someone could help me learn how to adjust the camera settings (if possible) so I can shoot in the dark and capture an aurora.
Not just settings
The first thing to understand is that this isn't just a matter of camera settings, but also one of technique and gear. So, I'd actually recommend staging your learning by getting basic night photography down before attempting the auroras, because they're a special case that requires a bit more thinking.
The good news here is that your camera is entirely capable of taking those shots. The one hard spec you might bump into is that your slowest shutter speed is 60s and that you don't have a bulb mode.
The bad news is your lens may not be suitable. If you only have a Lumix G Vario 14-42 f/3.5-5.6 kit lens, this could be tougher, particularly if you want to zoom in. If you have the Lumix G 20/1.7, Olympus m.Zuiko 25/1.8 or 45/1.8 it could be a breeze. You probably want a lens with a maximum aperture of at least f/2.8.
Stabilization
OIS can only eliminate camera shake blur for shorter shutter speeds, so
the first tool you'll need to add to the arsenal is some physical form of stabilization for the camera to eliminate camera shake blur. A beanbag, or a small travel tripod can work, or simply setting the camera down on a bench or fence rail can work, but a full-size, stable tripod would be ideal. This will let you leave the shutter of the camera open for a long time without creating motion blur from handholding.
You'll also want to use the timer on the camera so that pressing the shutter button doesn't jostle the camera.
Exposure Control
You're going to have to learn to adjust exposure. The reason for this is how the camera sets autoexposure. It usually meters the scene, then takes the average brightness level of the scene and sets that in the middle of the tonal range. Works great for most stuff. But in night time photography, when the scene is mostly black and your average brightness level is pretty dark, setting that darkness to be a middle-grey tone means you'll have overexposure. It's why you get brown skies in night shots when you want black ones.
To adjust exposure (also see pg. 83 of the manual), press the up (+/-) button on the four-way controller, and rotate the dial. You'll see the needle move on the meter to indicate which way you're adjusting the exposure, and the LCD should show you what you'll get. I'd also recommend trying to use S or M mode so you can set exactly the shutter speed you want, as well as so you can manually focus.
Focusing
Use manual focus. Your camera autofocuses by something called "contrast-detection". That is, the camera uses the contrast between pixels to determine when something's in focus. At night, there's not a lot of contrast, particularly if you're pointing the camera at an all-black sky. So it can't focus. This inability to be focused is why your GF5 won't take a shot and pops up that red square.
To focus manually, go into the [REC] menu, and set [FOCUS MODE] to [MF]. You'll probably also want to go to the [Custom] menu, and set [MF-Assist] to [ON]. If you have MF-Assist on, whenever you're in manual focus, and you turn the focus ring, then the LCD will show you a magnified view of your focus point to help you with accuracy.
Auroras
Once you've got all that down, then consider tackling the auroras. For specifics on shooting auroras, see: What tips and advice do you have for photographing the Aurora Borealis?, and the aurora-borealis tag.
The main thing is that auroras are a faint source of illumination and they move, things in combination that make them a harder-than-average subject. You may have to find someplace that's not light-polluted to shoot from.
You may also want to bone up on the basics of exposure. Bryan Peterson's book, Understanding Exposure is a good starting place.
