The Analog Basics
Modems
Now for the connection technology that everyone knows about - modems. 56kilobits/second is about as fast as modems are ever going to get, due to the technological limitations of analog and copper telephone wire. They've come a long way from the days of 300 baud (bits per second) modems (you old timers might know them - the ones where you had to place a telephone receiver on them).
Modems are the simplest way of connecting to the net, because most computers come with a modem built in, and if they don't, they're very simple to install. There are a lot of advantages to using modems, mainly cost and convenience. It's relatively easy to find a local Internet service provider by checking the yellow pages, or to use a nationwide one (AOL, Mindspring, Netcom, AT&T Worldnet etc.). Monthly fees range from $10 to $25, and some ISPs are even free (but you have to put up with tons of ads). There are just a couple of things that people should know about modems in general before deciding that they need to upgrade.
"Winmodems"
First of all, not all 56K modems are the same. Some do not contain their own on board processor to handle the overhead of modem operations. These kinds of modems utilize the CPU to handle these tasks in order to make the cost of the modem cheaper - colloquially this type of modem is called a "winmodem," even though the 3Com/USR Winmodem isn't the only one that does this. The Diamond Supramax is another example of a modem that taxes the CPU. Basically if you paid $50-$60 or less for it, chances are, you're using a "winmodem."
A lot of gamers hate these winmodems because supposedly they tax the processor to the point that it hurts your framerate and your ping in first person shooters. This might be true if you're using a first generation Pentium or possibly a Pentium MMX, but I have a hard time believing that a Pentium II or even a Celeron would notice a performance hit from a winmodem. Still, some hard core gamers swear against winmodems and avoid them like the plague.