Of course you want to test your camera for leaks, but I'd recommend starting with your darkroom setup. You want to know right up front if your box of paper has been fogged in the darkroom when it's been opened; not knowing this will throw off all subsequent tests.
If you have a changing bag, try removing one sheet of paper from the box in the bag, then remove that paper in the dark room. Then do the fog test for darkroom leaks. There's two ways to do this; the easy way is to simply keep one part of the paper covered by an opaque object (a coin, etc.) and leave the paper exposed in the darkroom under "safe" lights for at least 5 minutes. Then process the paper normally. The other way is to faintly flash the paper with white light (like from an enlarger for a few seconds at the smallest aperture setting), then do the same test with a coin over the paper; this second method is more sensitive for subtle leaks or fogging from safelights.
With either test, if you notice a density difference on the paper between the covered and uncovered parts of the paper, then you have a fogging issue.
There's also the possibility that the paper in the box is already fogged. The only easy way I know to test for this is to put the box of paper, scissors and a daytank in the changing bag; remove one sheet, cut off a strip and place it into the daytank; seal the box of paper and daytank before removing your arms. Then process the paper in the daytank. You can then compare the density of the paper strip and try comparing its tone against the backside of the paper strip, which should be pretty close to the same shade of white.
Once you know that your darkroom and safelights are good, then you can proceed with testing your camera for leaks. I've found with pinhole cameras you can often see the leak by illuminating one side with a bright articulating desk lamp in an otherwise dark room, and put your face up close to the insides of the camera, checking the corners and edges and seams for light. Of course, you can't check the camera's door or lid this way, unless the camera is big enough to fit inside(!), so you'll have to do a leak test by loading a sheet of paper into the camera (in your now safely-proven darkroom) and leave the camera, shutter closed, out in the bright daylight direct sun for an hour, changing the orientation occasionally. You should see fogging on the paper after processing.