There are some websites that are blocked in our work network, particularly, YouTube. I have an internet connection at home and I want to be able to make my work computer use or connect to the internet of my home-computer so that I'd be able to access YouTube. How would I go about doing that?
You can use VPN's like LogMeIn to access your home computer. But there are several issues regarding this.
As John T said, it isn't recommended trying to circumvent IT policies. They are there for a reason. To increase productivity and to protect the internal network for nasty nasty worms, viri, malware etc. You accessing your home computer without permission presents a security risk. I've known people to loose their jobs for doing such a thing.
Also, for you to use a VPN, don't expect quality video/audio as you would at home. You will probably not be able to watch anything or listen to anything due to latency from work to your house. Also, you need to know what ports are open and available to you at work for you to do this. If they have blocked websites, I can almost be certain that they have blocked a whole load of ports, to stop people like you doing such a thing.
Instead of trying to sneak past the IT guys with this one, ask if they are willing to set up a secure VPN from work to your house. Honesty is the best policy, even with IT policies ;)