I'm not home very often, but when I am, I would like to be able to browse privately. I believe my home network is monitored for my younger siblings, but I'm not sure specifically how. If I use Tor, is there any way that which sites I visit can be tracked?
Tor helps with protecting your identity from the web server by routing your requests through a network of other computers.
Assuming you have Tor running as a local web proxy on your own computer (the usual setup), then someone monitoring your local network should see web requests only to the Tor network and not the final destination.
That said, if they have access to your computer or are standing behind you, they can still see what you are browsing or look in your browser history.
Keep in mind that routing traffic through Tor tends to result in very slow browsing (they need more volunteers to help route other people's data in the Tor network), so viewing web pages that have content other than simple text tends to be a frustrating experience.