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In the U.S., it is generally legal to use a hidden camera to record footage without a person's consent--provided that you are filming in public or within your own home. Many states have passed laws against filming people in spaces where they have a reasonable expectation of privacy, such as bathrooms or personal bedrooms.  It is generally legal to use a hidden camera in the workplace, as long your filming pertains to a business concern. Don't film someone at work without their consent in order to settle a personal dispute--unless you're ready to risk legal consequences.  Laws vary between states and countries. Research the laws for your area before you record audio or video of anyone without their express consent. If you are planning to distribute the footage, sell the footage, or use it in court, then it is extremely important that you follow the law. If you are only planning to use the footage for personal entertainment purposes, you may not need to worry so much. Run a web search for "free webcam recording program" and install the software onto your computer. You may be able to use Windows Movie Maker or iVideo, if these are already installed on your computer. Search the Start menu (bottom left-hand corner of the Windows desktop) to figure out whether you have a program installed. When you leave the room, or when you are ready to start recording, boot up the recording software and click "Record". Cover up the USB cord with something so that it isn't obviously running to the hidden camera. Books, papers, or a jacket will do--anything that looks natural. Be subtle; only do this if you typically keep a webcam next to your computer.  Keep in mind that while this may be a more straightforward approach, the snooper may be more suspicious if they notice a camera point at them--even if they don't think that it's turned on. Be sure to turn off, cover, or disable the LED light that shows that your webcam is running. The "recording" light may tip off a snooper that they are being filmed. If the screen is open and the snooper can see the webcam feed, they will know that they are being recorded. You have to be sneaky to catch a sneak.  If you own a desktop computer, you should be able to turn off the monitor and leave the computer tower running. If you own a laptop, you may be able to put the screen to sleep while the recording program runs. You may also consider folding the screen down until the laptop is almost--but not quite--closed. The computer will look like it's off, but it will still be running. Leave the camera running when you think that it will capture what it needs to capture. If you're not sure, leave it on as often as possible. If time goes on and you don't capture anything incriminating, reconsider the situation. Was the snooping a one-time thing? Has the snooper found a way to sneak around your camera?
Be aware of the law. Download a webcam recording program. Hook the USB cord up to your computer. If you already own a webcam, consider simply using your existing camera to take the footage. Make sure to turn off or darken your screen. Keep recording until you get the footage you need.