Photographing the moon in general can be difficult, as at any reasonably long focal length that will capture useful detail, the moon literally races across the sky. Using a telescope with a camera adapter will probably provide better results than a telephoto camera lens, however both are options. A telescope on a proper mount will likely provide much greater stability and more framing/focusing options than a camera with just a telephoto lens.
The best advice I can give if you use a telephoto lens is to use one with some kind of image stabilization. It will make the near-impossible task of framing and focusing fairly easy. Just remember to half-press the shutter to let IS activate before actually triggering an exposure...otherwise you are guaranteed to end up with ghosted or fuzzy shots. I also highly recommend using the live view feature of your camera, fully zoomed in, to do your focusing. Trying to clearly focus the moon with only the viewfinder can be extremely difficult, and its hit and miss at best. A long focal length, 300-400mm, will give you decent magnification that will capture useful detail. The image below was composed of shots taken with Canon's EF 100-400mm f/4.5-5.6 IS L-series lens, at 400mm. Longer focal lengths magnify any kind of camera shake, so a cable release is pretty much a must have. The more stable your tripod the better, especially if there is any wind, as at 400mm, even wind vibrations can ruin a shot.
Regarding exposure, you might have some trouble here. A partial eclipse will have a brightly lit sliver, and that is going to create a contrast problem. As you can see from the image below of the recent total lunar eclipse on this years solstice, the second exposure had to overexpose the sunlit crescent in the second exposure to show any kind of detail in the dark part of the moon.
Copyright © 2010 Jon Rista
With a partial eclipse, you'll have to make the trade-off between exposing the eclipsed part, vs. exposing the sunlit part. If you have a camera with sufficiently high ISO performance, you might try shooting at relatively fast shutter speeds, and do some kind of HDR or Exposure Fusion to get both the sunlit and eclipsed parts properly exposed. You would probably need at least 1/20th of a second exposure, spaced very close to each other, to achieve such a thing. (My camera has terrible high ISO performance, so I was unable to attempt any such thing.
Finally, when photographing an eclipse, especially during winter, its best to have a lot of patience and a warm car. The night I took the eclipse shots above, there was a wicket wind chill. An eclipse takes a while to occur, and you'll probably want to take a good long sequence of shots to show the progression of the eclipse. You'll probably hop out of the car, frame, focus, and snap a few shots, then hop back in the car to wait a while before the next set.
And with that: Best of luck!