How do you connect a hidden camera to a computer?

Analog Security Cameras are connected to PCs via DVR Capture Cards, such as the ones seen here: http://www.apexcctv.com/c-23-dvr-cards.aspx

You take the BNC-style connection from the security camera and plug it into the BNC connection coming off of the DVR Card. Most of the time you'll need to run additional cable between the two.

From there, you can use the supplied software to view & record the CCTV footage.

As a general warning, all DVR cards aren't meant for all PCs, and compatibility must be checked before you commit to a purchase, if that is what you are looking to do.

Network (IP) Security Cameras are accessed over a network via a PC. For this type of camera, you need a Ethernet hub or switch to connect the cameras to via RJ45 Ethernet cable, then you can log into the camera's specific IP address, as long as you are on the same network. To log in remotely, via the internet, you need to set up more advanced settings - but that's for another question.