That depends on the physics of the portals. Does temperature travel through portals? If on one end, the pressure is lower or higher than on the other end, will they try to even out? (So, if one is in space and the other is on Earth, the portal wouldn't act as an orange or blue colored black hole.) Can portals be shot through portals?
If the answers are "no, no, yes," then the following would happen:
I would go outside, aim the portal gun into the sky, and fire. Then I would go down into a basement or secluded room, and put a portal on the wall. First, I toss up a Geiger counter to check for intense radiation. If there is intense radiation, reportal. If not, I toss up a video camera attached to a very, very strong rope. Jiggle the camera about a bit. And then I have modded gardening tools, so that there's two right angles in the shafts. Gather samples of dirt and such from wherever the portal is. Shoot portal directly through current portal and repeat until I get really bored. Then I would clear the portals. Post a whole bunch of stuff on the internet about me doing it, and that if it suddenly disappears, we know it's a cover-up. Then I put on portal up in the sky again, but don't put a second portal anywhere. Then I send half of each sample and the portal gun and copies of the videos to NASA.