Does using The Onion Router prevent my Internet Service Provider or system administrator from seeing what websites I visit?
That's really two questions. The "sysadmin" part requires more information. If it's a corporate PC, it will depend a little on how locked down it is. If the sysadmin enforces specific DNS and proxy settings, you may be hosed, but if there is no proxy, and you're free to install and configure TOR, you're pretty much good to go.
The second part, relating to your ISP, is a little more straightforward. Using TOR, your ISP will no longer be receiving your requests for the web sites you visit, and as such will stop them tracking the sites you visit. So, in general terms, yes, TOR hides this info from your ISP.
However, TOR traffic isn't encrypted the whole way (thanks Lazy Badger), so malicious or poorly configured exit nodes could be snooping on your traffic, so you're not protected from absolutely everyone.
If you're simply trying to reduce the amount of info you voluntarily give to your ISP, you could change your DNS server entries, although you'll then be guiving your DNS request info to some other party, unless you want to host your own DNS server. As an aside, it may be worth doing this anyway, as, depending on your ISP, there may be a speed benefit to using DNS servers other than your ISPs.
You might like to have a look a a DNS benchmarking tool to see how your ISP does here, e.g.: http://www.grc.com/dns/benchmark.htm
For the system administrator: NO
(assuming the system administrator has administrative rights on your pc, just like a corporate system administrator would have)
The sysadmin could for example easily install software that tracks your key presses and/or monitors your screen content. Both will reveal what sites you visit. Even if you don't think your sysadmin is so malicious, there could for example be a browser plugin that checks whether corporate proxy settings are honored and reports any deviations.
For the ISP, I agree with the other answers.