From Earth, we can detect extrasolar planets by a number of methods; primary are detecting the wobble in a star's motion caused by a large orbiting planet, and the dimming of the star's light as the planet passes between it and Earth. Neither of these seems very amenable to quickly finding planets, nor to finding planets while at the star.
So: You're looking for habitable planets and have used your hyperspeed device to reach a distant G-class star. Now what can you do to find its solar system? I'm trying to see how to do this relatively quickly (on the order of weeks), with reasonable extrapolations of current technology (except that we can move really really fast). Scaling up the methods we currently use to find e.g. Kuiper belt objects don't really seem amenable to this time frame; could we even do a complete astronomical survey in a few weeks? Would it give us enough information to find the planets?
We're looking for habitable planets, so I'd be OK with just looking in the Goldilocks zone, but finding all of the planets would also be interesting.
EDIT: It looks like the simplest method would be to scan the sky from a bunch of points in (or near) the system, then compare the pictures to 3D-locate nearby points. I'm still not certain of the optical constraints here, though. Could someone who knows something about astrophotography comment on how big / sensitive the camera would have to be to pull this off?