There are a bunch of different proxy configurations. The two types that are relevant for you are HTTP proxies and VPN service.
HTTP proxying is done by your browser, so it sends only browser traffic via the proxy server. Most elements on a web page will be sent via the proxy server, but there is a notable exception - video on the web is usually built on top of adobe flash, and the flash player's video connection bypasses the proxy. The net result is that using a HTTP proxy probably won't work for viewing adobe flash videos (you could try it out to see if it works first).
VPNs work by sending *all* traffic via the "proxying" server. This means that adobe flash video works over VPNs. Many VPN services will work using the built-in PPTP support in Windows/Mac, while other services will require you to install additional software. All public VPN services that I know of are paid services. You can find them by doing a web search for the term "vpn service".
One more thing to note - country-restricted web video services enforce that restriction by checking your IP address against an IP database. Such IP databases usually also include lists of HTTP proxies and VPN services, and the video services may block access from those proxies/services (to... ummm... well, to prevent exactly what you're trying to do). So even with a working proxy setup, you still may not be able to view that video. Again, you will need to try first, and maybe try different providers, as the IP databases usually are far from complete or accurate.