To watch the TV3 online programmes you need to access their media site called 3Player. This allows you to stream the majority of TV3 shows apart from a few exceptions. Although you'll need to be in the Republic of Ireland to view these shows.
This is because TV3 has like the vast majority of broadcasters, restricted their content to specific countries - usually the place where they are based. The technology used is called geotargeting and is used for many purposes on many different sites. TV3 looks up your location when you first access the web site, and this determines what you can access.
If you're outside Ireland, you'll need to use a proxy or VPN server to hide your real IP address and watch TV3 online. This is a server which sits between you and the website you visit, relaying requests when they're made. The website will only see the IP address of the proxy, so you can use this method to access any site on the web. This video demonstrates a service called Identity Cloaker which comes with a global network of servers designed to hide your real IP address and encrypt your communications.
There are quite a lot of these VPN services available now, so there's certainly a lot to choose from. Which one you choose will depend on your particular circumstances. Make a list of the sites you need to access and make sure that the company provides a server in that location, be sure that the service provides many more US and UK servers as these are by far the most popular. Speed will suffer if there aren't enough servers and watching video via a slow proxy is a painful experience.