The easiest and cheapest way is to get an Easycap DC60+. Just search the name on eBay. And be sure that it's the DC60+, not DC60. The DC60's drivers are terrible and only work half of the time. I used one of these for nearly a year and I only spend around $20 on it.
Then I felt the need to upgrade, so I purchased an Avermedia HD DVR. It's a PCI-E capture card that supports up to 1080i via component or HDMI. It's great for HD video game systems. I've been using this for about a month and the quality is excellent!
I use Flash Media Encoder to stream mainly.