A field guide to the boxes, cables and wires cluttering up your space
Cords/Wires/Cables
Ethernet (network) cords have clear plastic connectors that are almost identical to phone jack connectors, but slightly larger. They can be used to connect you to your home network and, ultimately, the Internet.
Coaxial cable is the cable in “cable TV” or “cable modem”: it’s round, roughly the diameter of a pencil, not very flexible, and often solid black or white. The connectors are round metal screws with a thin metal rod sticking out from the middle.
Power cords & adapters come in many sizes and shapes, are usually black, and should always be kept with the device they came with, as different cords supply different amounts of juice. (A silver Sharpie marker works very well to label them!)
USB cords are used to connect devices like printers, external hard drives, cameras, and other do-dads to your computer. USB cords usually come with one squarish and one flat connection, though the squarish end can also be a tiny trapezoid shape (typically for small devices like cameras).
VGA / DVI / HDMI cables are used to connect your computer to your screen (or your laptop to an external screen, or, in the case of an HDMI cable, pretty much anything to your new TV). The cables are usually round and black, and all have similar widths. The ends are different: VGA and DVI cables have groups of pins in a metal housing at each end, and usually have screws to secure the cable to its endpoint. VGA ends are smaller than DVI ends, and have fewer pins layed out in overlapping rows. The ends of an HDMI cable look rather like the rectangular end of a USB cable, but are wider and faintly trapezoidal.
The New York Times offers a handy guided slideshow showing what different cables look like and connect to.
Network Boxes
Cable modems usually have just 3 connections, each a different shape: a round, screw-type connection for the coaxial cable; a square ethernet jack for connecting to the PC or router; and a power cord connection.
Routers allow you to have more than one internet connection through the same cable modem. They can be wired-only or can include wireless capability as well (wireless routers usually have stubby antennae that can be moved around). Both types ususally have four “ports,” or outlets, numbered 1-4, each with a corresponding light on the front of the box. These ports are like the outlets on a power strip: you can use any outlet you want, they all do the same thing. Routers also have one different port, sized exactly the same but usually placed a little apart and variously labeled “WAN,” “ Internet,” or “Uplink.” This is used to connect the router to the cable modem. Last, there’s a spot for the power cord.
Combination router/modems that combine both functions have become significantly more common in the past couple of years.
Diagram of Computer/Router/Cable Modem Connections

C. A coaxial cable connects the cable modem to a coaxial wall outlet.