I want to try my hand at off-camera flash for some indoor portraits. How should I trigger the speedlite (Canon 550EX)? Should I go for wired or wireless? What's the difference between a TTL cable and a PC cable? What's the cheapest option to get me started?
For off camera lighting with strobes there are several options:
The best solution in general is either the Pocket Wizard wireless triggers, or the Radio Popper wireless triggers. Both are highly regarded, used universally by pros and amateurs alike, incredibly reliable and perform very well. Newer systems preserve TTL data, passing the information from your camera to the strobe. Older systems were typically used with manual flash settings. These triggers also have multiple channels to prevent interference, and to create "strobe" groups.
Unfortunately, they're not cheap, nor are they really necessary for a single off-camera flash setup.
So that leaves with some other options to try.
There are ebay flash triggers, that are roughly 10x cheaper that have okay performance, but lack the bang-bang-bang reliability, distance, and features of the pocketwizard/radio popper triggers. But, for someone who is just starting out, the price point is very good.
TTL cables allow you to transmit TTL data, where as the PC cable is just a dumb sync cable. TTL data contains data to for auto flash exposures. If you're looking to do manual flash settings, then a simple PC sync cable should work.
Canon and the 550ex also support wireless IR triggering, when paired with the ST-E2 transmitter. Since this setup is IR based, it does require line of sight. It works relatively well indoors, but is not as cheap as ebay triggers.
Optical slaves trigger the flash when it detects a flash pulse. This is of no use when you use a single strobe, but in multistrobe environments optical triggers are a cost effective way to trigger them.
The big advantage to wireless is the freedom to reposition your strobes without worrying about cords. Wired setup is far cheaper, and more reliable than the cheaper radio triggers, but with the added hassle of connection.
I highly recommend heading over to strobist and going through his lighting 101 series of posts. It's incredibly informative and gives great insight into how to get started using off camera lighting.
Alan's answer covers the wireless option (and was posted while I was typing) so I'll restrict this to the wired options.
Let's start with what you probably don't want. The PC cable option is the cheapest possible -- until you take into account the flash-capable light meter you're going to need in order to make it work the way you'd like. There was a time when that would have been a reasonable option, back in the days when a good external flash could work in stand-alone auto mode. That is, the flash would have its own built-in meter, and as long as the film ISO was set on the flash and the meter was pointed at the subject you could more-or-less fire and forget. Your flash doesn't have its own flash meter; it only operates manually or using TTL metering (TTL means "through the lens", so it's the camera that does the metering). A PC cord can only tell the flash when to start firing, but not when to stop, so you'd be stuck with manual mode (setting the power level on the back of the flash). Manual mode is the most versatile way to operate, but it does involve that rather expensive flash meter I was talking about earlier (or a lot of test exposures for every single setup you use).
A TTL cord lets the camera talk to the flash as if it were sitting safely in the camera's hot shoe. You get the same degree of convenience you'd get with an on-camera flash, but with the benefits that come with a different lighting direction. At one time, TTL cords were the only practical way to get TTL control with an off-camera flash, and they are still the most reliable if you are using a flash bracket. They are God-awful expensive, though (at least if purchased new with the Canon name on the box), and they tend to be a tripping hazard when they aren't acting like a short leash if you are using, say, an umbrella setup or a mini softbox on a lighting stand.
If you have a Canon EOS 7D, then the master is at the built in flash, and you can use the 550ex as a full ETTL off-camera wireless flash.
Syl Arena's Speedliting.com has great information on all you wanted to know about controlling an aff-camera Canon flash.
Go for wireless radio. A lot has changed in four years. :) The cheapest and best option these days would be to get manual radio triggers, and possibly to not use the 550EX at all, but to get a cheap manual flash with remote power control (e.g., a YN-560III/IV and YN-560-TX or Lumopro LP180R and and Phottix Odin/Stratto. The days when PocketWizard was your only option are long gone, thanks to the Strobist.
Cheap manual-only radio triggers these days are liable to cost even less than a PC sync or TTL cable, and while "dumb" optical slaves may be cheaper, when you factor in hotshoe/flash foot adapters to hook up the slave, the cost comes out roughly the same. And radio triggers have advantages in terms of range, usability outdoors in daylight, and no line-of-sight requirements over optical triggering.
The difference between a PC cable and a TTL cable is not only the connectors, but also the number of signals the cable can communicate between the flash and the camera. A PC cable has a connector similar to coaxial cable--the outside ring is ground, the inner pin is the sync signal. So, all that can be communicated is the sync (fire) signal. So, it's a "manual only" connection: no TTL, HSS, camera menu control, etc. Just firing in sync.
A TTL cable has a hotshoe and flash foot connections, and will be brand-specific, so that the pin/contact placement matches that of your camera and flash. Since all the signals of the flash and hotshoe are communicated, everything you can do with the flash on the camera's hotshoe can be done with it on the cable. However, most TTL cables are designed to simply put the flash on a bracket, and are relatively short. To use one for off-camera studio setups, you may have to find a specialist seller, or hack your own (or buy) a CAT5 solution.