Visit the website of the network that airs the television show you missed. You can also search for the particular show and follow the link to the network.
Find the link for the series and look for streaming video. Full episodes are not always available, but there are often video clips.
Download any programs that are required to view the episode or clip.
If you don't find the program you want, visit streaming video sites such as hulu.com or fancast.com. Some networks have partnered with these sites to host commercial-supported episodes.