The SSH tunneling in Clemens' answer will work for one specific website, with caveats... if the site does virtual hosting, where the content depends on your HTTP request pointing at a specific hostname, simple port tunneling won't work. And it will only get you to the one site.
A more robust solution is to use OpenSSH dynamic port forwarding. The command would be:
ssh -D 1080 ssh-server.example.com
Next, set the browser on your client to use a SOCKS proxy at 127.0.0.1, port 1080.
Now, regardless of which site you're visiting, all of your browsing activity (including DNS lookups) will use the remote server.
More detail is here: SSH/OpenSSH/PortForwarding: Dynamic Port Forwarding
If you need to switch frequently between browsing normally and browsing through the remote SSH server, look into installing a plugin for your browser to do fast proxy switching. There are a lot of them.