There are a variety of ways to do it, for example:
1. Using your cell phone's camera (360 still photos & side-by-side video)
2. Using a dual-camera setup (3D)
3. Using a 360 camera setup (360 video)
4. Using a VR camera (multiple cameras built into one rig)
Stuff like Homido Player has a video recorder that translates the footage into side-by-side video for you to watch in your Cardboard. A dual-camera setup is better because then you get real 3D (because it's two pictures that are offset so you get the 3D effect). You can also do a 360 camera rig like with a bunch of GoPros:
http://www.360heros.com/
https://gopro.com/news/happy-sweet-sixteen-introducing-gopros-360-camera-array
There are a lot of VR cameras starting to come out. Nikon just beat everyone out of the gate with a VR action cam at CES:
http://www.roadtovr.com/nikons-4k-360-camera-rugged-ready-maybe-not-vr/
Or the professional Nokia Ozo for $60k, which is a bubble of cameras:
https://ozo.nokia.com/
VRSE shot "The Displaced" using eight GoPros on a pole. The Odyssey from GoPro holds 16 cameras for $15k:
http://www.theverge.com/2015/9/8/9261745/gopro-google-odyssey-virtual-reality-camera
So, there are a lot of ways to do it. The Viewmaster comes with a Destinations app that you can download on your phone, which uses 360-degree still photos to let you look around your location - you don't need a 360-camera rig for that, just an app that does panoramas. The Google Cardboard app itself actually lets you do that - instead of just Pano, it's a full 360 shot that you spin around for:
http://www.wired.com/2015/12/google-cardboard-camera-app/
So the equipment & capture method depends on what kind of still or video footage you want to create. I think a really good example of what you can do with VR is VRSE's "Take Flight" experience, which has high-end photography (well, video - well-lit floating actors) & a neat flying/falling/floating feeling, plus a bit of CGI & stuff. The amount of work & planning to execute stuff like this in VR is insane though, but I think it would be really fun to shoot a movie like that (whereas I'd probably never ever shoot a 3D movie - I did like Avatar, but literally nothing else I've seen in 3D has been good so far - but VR is a very immersive experience & you can do some really neat stuff in it).