How do I setup a remote server that I can use as a SOCKS tunnel?
 

I am a volunteer computer technician at in a local community building. Our Internet connection comes directly from the school that is connected to our building. The school has Smoothwall installed on one of their Cisco servers and almost every website is blocked. Even ntp is blocked, if the clock on one of our systems is out of sync we have to set it manually.

My laymen understanding is that all traffic is transmitted over an encrypted tunnel via SSH. As I understand it, the remote server is functionally similar to a Tor exit node.

Are there any decent tutorials out there explaining the process? For a test run, I'd like to setup a system whereby I proxy to my home network. Since I'm not familiar with SSH I've run a couple of searches but the tutorials I've seen online don't clearly explain what I need to setup on the remote server side. They only explain what I need to setup to connect to the remote server.

I'd look into pricing for independent connectivity for your organization in your part of the building. Depending on the options in your part of the country, you might be able to find something affordable. Some 3G/4G modem service might be available without a cap and that can be plugged into your group's router and moved where it is needed.

Alternately, what can be done about getting the school to fix their badly misconfigured filters? What kind of level of service agreement do you have with them?

About the tunnel question, OpenSSH's client can make a SOCKS proxy, look at the -D option in the manual page.
That would set up SOCKS5 tunnel to the outside via outside.example.com. You'd connect to it via port 4558 on localhost. Not all applications support SOCKS however. For some of the others, you might be able to use the utility proxychains.