These elements include your camera's shutter speed, the speed at which you trip the shutter, the things you record or choose not to record, and the frames-per-second that you choose in your editing software. I'll assume we're using an intervalometer, such as the Canon Timer Remote Controller, although other devices can be used, and you could even do the time lapse manually. Let's go through the elements in more detail:
1) Camera's shutter speed: generally speaking, you want to create a slight blur when doing a time lapse, in order to show motion naturally. This depends on how fast your subject is moving, but for many common subjects - i.e. people walking down a street - you need at least 1/30 of a second to capture a certain amount of blur. Any faster, and the subject may become too sharp; any slower, and the subject may become too blurred.
2) Speed at which you trip the shutter: this depends completely on how quickly the subject is moving, and what effect you want to create. Is the subject a wide view of Times Square? Then you might want to trip the shutter every second, to capture the hustle and bustle. Then again, if your subject was something very slow-moving, like clouds drifting across a sky, then you might want to trip the shutter once every ten seconds, or even once every ten minutes.
3) The things you choose to record/not record: this is an interesting element of time-lapse photography. Imagine that you want to do a time lapse of a concert, but in the middle of the concert, the musicians take a long break. You wouldn't want to record this part, right? There's no reason why a time-lapse has to be totally continuous. It may be a good idea to start and stop it at various points, to get the desired effect you want.
4) Frame rate when editing: now that you've got all your photos and put them into an editing program (for example, Quicktime Pro), you must decide on the frame rate. You can try 15-30 seconds, or any other time you like. You may realize that your time lapse is more effective if it's sped up, or slowed down.
The following time lapse was made for a recent client. The objective was to record an art exhibit on a busy Tokyo platform. I had to record it from the other side of the tracks. It was a nerve-racking experience, with security guards just feet away - in Japan, security tends to be very tight, and taking pictures in public tends to be frowned upon. I decided not to use a tripod, because I would probably be asked to leave if I did so; instead, I brought a large, empty gear-case, and put my camera on top of it, then started the time lapse. Surprisingly, nobody stopped me, and I got the time lapse you see. Since the two trains were obscuring the artwork the majority of the time, I stopped and started the time lapse continually to minimize their presence.
Time Lapse For Art Below from Benjamin Parks on Vimeo.