remember they have no concept of what humans have named stars and clusters
You need to find markers that are easily explained and easily visible. This is likely to require a lot of knowledge of astronomy.
You first find the Crab pulsar (the brightest(?) gamma/X-ray source in the Galaxy) and tell them head to there. That gets you relativity close, galactically speaking. Now your within ~2000pc from Earth. You have a problem of course if you are so far away that the location hasn't seen the Crab explode yet (assuming some sort of FTL technology).
Once your within a few thousand light years of Earth you just need to pull out your copy of the Gaia database and start matching stars based on stellar properties (their total luminosity and spectral colors) with the stars you can see. As your only a few thousand light years from Earth, the stars properties wont have changed much compared to what Earth observed.
If you didn't pack a copy of Gaia, then finding other "interesting stars" will help. Betelgeuse is few hundred parsecs away (a very bright very massive star), Sirius (a star with a companion star that is the size of a planet (a white dwarf) in a 50 yr period) which is only a few light years way from Earth. Once you found Sirius then its a case of saying looking for the star with multiple planets, where several very large planets are in a very wide orbit, and several smaller inner rocky planets. Earth is the one with water.
There are a number of questions about interstellar navigation in general and findng Earth in particular, in the Worldbuilding Stack Exchange. I have answered some of them.
I suggest a four step method to find the way back to Earth from any place within a hundred million light years in my answer at:
If you have traveled into deep space, interstellar space, in an Earth ship, you should have at least some basic knowledge of what Isaac Asimov called "galactogrphy", the "geography" of the galaxy.
So you should know the coordinates of various interstellar objects in one or more coordinate systems, and/or have books or computer files with a lot more coordinates.
Earthbound astronomers use several celestial coordinate systems such as the equitorial, elliptic, and galactic coordinates, to express the directions to various objects as seen from the Solar System.
It is possible to map the positions of various objects in a 3 dimensional array, if the distances to those objects are also known.
The space traveller can tell the alien that there are 360 degrees in a full cirle, 60 arc minutes in a degree (21,600 minutes in a circle), and 60 arc seconds in an arc minute (1,296,000 arc seconds in a circle). So that should help the alien convert your angular measurements into his angular measurements.
The Earth astronomical coordinate systems all have a latitude of zero at their equators and ranging from plus 90 degrees to minus 90 degrees at their poles. And they have longitudes ranging from zero to 360 degrees - except for the equatorial system which is divided into 24 hours of 15 degrees, so that each minute is 15 arc minutes and each second is 15 arc seconds.
And if the space traveler is stranded soewhere in our galaxy, it should be a lot easier to find their way home if they remember the coordinates of various highly luminous astronomical bodies.
For example, the coordinates, and thus directions from Earth, to the center of our Milky Way Galaxy, the center of the Small Magellanic Cloud, the center of the Large Magellanic Cloud, the Center of the Andromeda Galaxy M31, the center of the Triangulum Galaxy M33, and the center of the great galaxy M87 in Virgo, should be more than enough data points to locate a relatively small region of our galaxy wher Earth should be.
And if he remembers the distances from Earth to those astronomical bodies the alien can make a 3-D computer image with spheres around the centers of those objects at the distances mentioned by the human. The spot where the spheres intersect should be the region of the galaxy where Earth is located.
How will the alien know how much distance is in an Earth light year? Maybe the many advanced instruments a human space traveller has will include a timepiece. Or maybe the alien will time the human's heartbeats and compare the rate in his time measurements with what the human thinks is the rate in human times mesurements. Maybe the human will count out approximate seconds and the alien will time them to get the approximate ratio between time measurements.
And then it will be easy to calculate how far light will travel in an Earth light year. A light year is the distance light travels in a Julian calendar year 365.25 days long. And calculating the number of seconds in a year is so easy that I once calculated it in my head while walking to elementary schhool. Anyway, you can use a calculator to find that there are 31,557,600 seconds in a Julian calendar year.
And of course the alien should have a good idea of how long an Earth year is if the alien is also a carbon based, liquid water using, oxygen breathing, lifeform. In that case his planet would have to orbit its star at a distance where the planet would have a temperature where water is liquid in many regions.
Stars vary greatly in luminosity, and so their habitable zones where water would be liquid on a planet vary in size by thousands of times. But there is a much smaller range of stellar luminosity and thus size of habitable zones in stars which are otherwise compatible with habitable planets. The year lengths of habitable planets should vary by only a few times.
See pages 67 to 72 at Habitable Planets for Man, Stephen H. Dole, 1964:
And if the human tells the alien that the angular diameter of the Sun is about half a degree as seen from Earth, that should help the alien calculate the approximate length of an Earth year. Habital planets of more luminous stars would have lower angular diameters of the stars and longer years, while habitable planets of less luminous stars would have higher angular diameters of the stars and shorter years.
And if the human has measuring devices the alien can convert human length measurments into alien length measurements. And if the human knows the length in human units of a parsec or a light year, the alien can calculate that distance in his measurements.
The borders and thus dimensions of our Milky Way Galaxy are rather fuzzy and vague, but if the human and alien societies use the same definitions, the ratio between human parsecs or light years and alien distances can be calculated.
If the human knows the absolute distances between Earth and the centers of the MIlky Way, Andromeda, Small Magellanc and Large Magellanic Galaxies, the relative distances between them and Earth can be found. And so the region of the Galaxy where Earth is can be located.
There are a few open star clusters within a few hundred light years of Earth.
Two of them, the Hyades and the Pleiades, and the red giant star Aldebaran, are almost lined up when seen from Earth. A line going toward the galactic center from the Pleiades past the Hyades and past Aldebaran will point close to the Solar System.
So once the relatively small region containing Earth is located, a search should be made for two open star clusters almost pointing toward the galactic center and almost in line with a red giant star. And travelling along that line toward the galactic center should make the constellation of Orion behind the ship appear more and more like it is seen from Earth.
So those are my ideas how a human space traveler with sufficient astronomical information could find their way back to Earth.
...how would you explain the location of earth in the galaxy?
I would first describe the two Voyager spacecraft to the aliens and tell them to go find at least one of them and bring it to me.
I would then ask them to study and decipher the drawings on the outside cover of the record, specifically the large "star-like" radial lines with binary numbers that represent various pulsar directions and frequencies in the neighborhood of Sol.
Of course I could also then ask them to back-calculate the trajectory from whence it came; which would be easier depends on how far we are currently in time versus how far we are in space from Voyager's origin. I haven't a clue how I ended up there so I'll give them both options and let them figure out which is best.
- An alternative to gold plated record?
- For how long will the Voyager records remain playable?
- Why did we send those golden records on Voyager crafts?
- Did Huygens probe carry any hint to help find its home planet?
- What technical challenges would be playing this LP in (actual) space?
The Voyagers and the solar system up to about 2018 from this answer to Where is Voyager 1 now (2021)?:
A third way. There are more roads leading to Rome. They probably have a teletransporter. How to feed it the right coordinates, whitout consulting the hitchhikers guide to the galaxy?
I would ask them (if I talk alien...) to beam one of them to my galaxy. With my knowledge of the universe this is possible. The universe would look very different for them but I could give the specifics of a Milky Way specific varying over time so they should be able to look for this.
The next thing I should ask is to teletransport one of them into the Milky Way. Once in the alien could orient himself by looking for the horse nebula or some other one the closest to Earth.
Once there he could find the coordinates of the Earth. To know the first object is the most important.
He could also surfe the Milky Way and look for the first radio signals that were sent from Earth.
When he beams himself back it is no problem to beam me back but I doubt if I would ask it! I would ask them to let me stay and beam my loved ones to me. But the again...