Your client is set up! Now for the browser. As I stated earlier, I'm using Firefox. However this technique will work with anything you wish to mask. I even use it for remote desktop connections, effectively giving you your own VPN.
In Firefox, go to Tools > Options > Advanced> Network, then click the Settings button under connections.
Figure 3: Firefox Network Settings
From here, select Manual Proxy Configuration, then under SOCKS Host enter an IP address of 127.0.0.1 and the port number you entered earlier in PuTTy (8080 in this example).
In the No Proxy for box, enter localhost, 127.0.0.1. I use both since some OS's have different addresses for the loopback. However, localhost is the standard name in most cases. Select the SOCKS V4 radio button. V5 might also work, but I've never tried it. Click OK.
Figure 4: Completed Firefox Network Connection Settings
Now enter about:config into Firefox. Enter network.proxy.socks_remote_dns as the filter and double click on the parameter to change the value to true. This will use your SSH connection's DNS, and not the one you're currently connected to. Even when using the tunneled connection, your browser would normally be using the local DNS server. Using the remote, tunneled DNS server removes the risk of someone looking on the DNS server to see the web pages you're viewing.
You're now done! You should be browsing the web using your SSH server. Remember you have to stay connected for this to work. If your shell connection drops, you will lose your Internet access connection in that browser.
As I stated before, this can be used for anything that lets you set a Proxy to connect to the Internet (which is almost everything these days). Most of the settings look the same as the ones above in Firefox. Just make sure to specify a SOCKS proxy.
Happy secure surfing!