Either tool is under the control of the holder of the account where the video has been uploaded (or by someone who has been given the authority to use that account).
However, imagine that you already have a complete script for a short video under fifteen minutes long (YouTube's current limit for uploaded videos from most standard account holders). YouTube's software can automatically synchronize the words in the text with the spoken audio. This saves a great deal of time and is the best way to provide the captions if you already have a complete transcript. (However, it will still help to read the "Captioning Key" and you may still want to use VideoCritter.org afterwards to make any needed changes; both are discussed below.)
The second YouTube tool is automated transcription, which uses Google's speech recognition software to produce captions and which generally inevitably produces errors. By default, new videos uploaded to YouTube are now automatically transcribed. If the speech on the video is clear and in unaccented, standard English, and if there is no background noise or music, chances are that the automated transcription might work fairly well at producing usable captions. The resulting caption file should then be edited to correct any errors.
Viewers do not see the automated captions unless they have elected to turn on the automated transcription by pressing the red CC button on the lower right hand side of the video, then clicking on "Transcribe Audio", and then on "OK" after they have been made aware that they are using a beta service.
YouTube began providing free automated transcription of all videos uploaded to YouTube early in 2010. (The service can also translate the English captions into different languages.) See:
For example, there are "style guidelines" and a "Captioning Key" about how to format the captions properly which is particularly useful to read. Many amateur captioners would do well to look over the Captioning Key. Although I'm a long time user of captions, I still saw tips there that hadn't been obvious to me.
There are other tools as well to caption videos or YouTube videos, which are mentioned in the above resource.
If you want the ability to caption any video in any language, check out http://DotSUB
I haven't had personal experience using any of these captioning tools. (Being hard of hearing, I'm usually not able to make out the dialog in videos in order to caption them.) Please feel free to share your experience using these captioning tools by posting a comment below.
Update: I've written this blog with the presumption that most people reading this blog would be interested in learning how to do the captions themselves. However, there are professional companies who specialize in providing captions for videos. See the comment below for more information. I've edited this blog to incorporate the corrections provided.