A PCI/PCIe capture card is one of the best ways to do it. However, a second best is to use a capture device that's USB.
Which device to get is up to you based on you computer's hardware specs.
I personally use BlackMagic's Intensity Pro to capture 720p 59.97fps. However, this can eat up a lot of space fast as it captures it uncompressed and requires a fast enough hard drive (SSD) or a raided set of hard drives.
Avermedia is another brand that I would suggest looking at for quality, but I don't have any personal experience although it's what Jaxel uses for his 8WayRun Streams.
For a USB option you can go the traditional Hauppauge HD-PVR device which will compress the footage before saving it to your hard drive saving you the process of converting them yourselves at the loss of quality to the video feed.
Lastly you'll need a video editing program if you want to do any sort of editing with them. Windows Movie Maker is a free editor that will take some of the basic codecs but has little in terms of allowing you to alter the output much. I personally use Adobe Premiere CS6 which is a general standard for video editing in the movie business.