Expanding further on my comment to another answer...
You remember part of the lyrics of "the galaxy song" from Monty Python's meaning of life (or otherwise have some reason to remember similar statistics):
Our galaxy itself contains a hundred billion stars; It's a hundred thousand light-years side to side; It bulges in the middle sixteen thousand light-years thick, But out by us it's just three thousand light-years wide. We're thirty thousand light-years from Galactic Central Point, We go 'round every two hundred million years; And our galaxy itself is one of millions of billions In this amazing and expanding universe.
This gives the approximate distance from earth to the centre of the galaxy as 30,000 light years, and also calibrates what a light year is for the alien's benefit as 1/100,000 of the distance across the galaxy.
So far this only gives us the (very approximate!) distance from the centre of the galaxy... but you also remember that the centre of the galaxy from our point of view is Sagittarius A*, and of course that the nearest galaxy to us is the Andromeda galaxy in the Andromeda constellation.
The relative position of the galactic centre to the Andromeda galaxy would greatly narrow down the search area. It would be even more useful if you can identify and remember the correct relative location in the sky from Earth's perspective of some other nearby galaxies to improve the triangulation and reduce the search area. In particular a comment from someone more familiar with astronomy than I suggests the Magellanic Clouds - being different distances away, they would only appear at the right apparent spacing from someone in a similar region of our galaxy.
Also, supernovae that you know about (where in the sky they appeared as viewed from earth, and when in earth's history they were recorded) could be useful as further triangulation points if they're ones the aliens also know about. If the aliens know exactly where and when in the galaxy the supernova actually occurred, then the number of years after the event that it was observed from earth would give a distance... but for many of these it could be uncertain WHICH supernova was the one we saw given that there are potentially thousands of [light-]years of uncertainty about the position we were observing from, and large numbers of supernova events that may be observable over such a time span. That could even make an interesting blind alley for the story - the aliens correlate the only supernova you can remember with one that hasn't been observed from earth yet.
The exact shapes of constellations would seem less useful initially, but once you've got an approximate location, the aliens' database could perhaps come in useful to reconstruct what an observer at various places in the search area might see (unlike the questioner who assumed planets would be known about, I'm assuming only the position and brightness of each star is known). This can also be correctly aligned (using the known positions of the galactic centre and andromeda galaxy) so that you know which constellation you should be looking for in which part of the sky as reconstructed from the star charts.
I could imagine it working something like this:
The aliens put together a database of all known stars with their brightnesses and exact positions and velocities to create a simulation of what the sky would look like from any specified position as of the time you left your home system (as other answers, they may need to send some probes to locations not to far from the target area to update their database). 840
They set you up with a few example view points. Every time the stars look totally different. Surely this is hopeless - you won't ever recognise anything. So many images have gone back and forth you can barely remember what you're looking for.
The screen is focussed on the view towards andromeda - one of the few common waypoints you could identify with certainty. The first try with Sagittarius was hopeless, as there are even more stars in that direction and you can make almost any shape you want (besides you can't remember the shape of that one so well).
After flicking between hundreds of random search points within the target area, suddenly "the projected view to Andromeda galaxy from this place kind-of looks a little bit like Andromeda, but really distorted and with stuff missing", then the alien lets you jiggle the stick a little, and a star approaches from the right side of the screen. You try to use the star to complete the picture, but it's still badly distorted. Looking at other parts of the simulated view from this place, nothing is recognisable. Disheartened, you think it must just be a co-incidence. The alien moves to a full 360 degree projection room and moves the simulated view point back and forth along the direct line to Andromeda. The star you picked fades almost completely out of view, and whichever way the alien moves the view, it gets worse. 758