Assuming you mean the Game Capture HD, you have two choices, assuming you're using composite cables: Either way, get a few RCA splitters (something like this), one side should go to the TV, the other to the Elgato, in some fashion. If you want to pipe the video directly into the Elgato (which cannot handle 240p well/at all basically) if you're using a Game Capture HD, you could either use the "Analog Video Adapter", which can take S-Video, or you could use the component adapter that comes with the Elgato, though it won't look great. If you're not using a Game Capture HD, or just want the signal to come into HDMI/be handled elsewhere you will need an composite to HDMI adapter (these work well enough to have a picture, but are trash, and again don't really handle 240p right), again, this won't look great. If you want a bit nicer quality, you *could* get something like an XRGB Framemeister, but that's a little overkill at this point, and still won't look very good. At the very least, get an adapter that takes S-Video. Otherwise, if you're using SCART/RGB input, you're generally past the territory where an Elgato is useful, but you could use an OSSC or XRGB Framemeister to get it to HDMI to get to the Elgato. I'm not really experienced with the RGB capture side of things, so if you're dealing with that, ask KevinDDR or DarkAries, they know what they're doing a hell of a lot better than me.
Aside from the 4 second delay, my Elgato handles 240p just fine. It even handles TAP and its strange frame rate. What exactly are you looking to capture? Nes or an arcade signal?
I'm by no means an expert on perfect capture, but one of the easiest ways to do it (provided your tv doesn't have video out jacks) is to plug your NES into an old vcr (you can find one at a thrift store for about $10) and connect the video out on your vcr to the elgato. Composite goes to red on the component dongle. Connect the VCR to your TV via RF. This setup served me well enough in a pinch during Extra Life last year when someone took my S-video cable home by accident. Mileage may vary.
