A good solution is to use openvpn with www.perfect-privacy.com. Perfect Privacy has openvpn configs set up for their entire server park.
If you don't want to install openvpn, you can still use Perfect Privacy via a SSH tunnel using the pre-installed software in puppy. However, I have found that this will occasionally drop the tunnel.
Another option is to use Tor and Privoxy. See: https://www.torproject.org/ There are .pets set up for this software.
Finally, if it is just for browsing, you can try ixquick and use their built in proxy server: http://www.ixquick.com/eng/aboutixquick/ It is very easy to add the ixquick toolbar to firefox and this can be setup for https encryption.