A character from 1920's England is unexpectedly flung into the distant past in a strange place. (It's around 1000 BCE in Mesopotamia). How can she discover roughly when and where she is? What key clues would she need to decipher in order to have some chance of figuring it. She knows something about architecture, and is a regular visitor to the British Museum, which may help.
For when she could be an astronomer and have access to good modern equipment, datasets, and computer simulations this may not be workable for your narrative however. The other option is that your protagonist is a history buff, this may mean fully qualified history professor specialising in the period they've stumbled into, which could be quite believable depending how they're getting moved through time. Or it could be that they're an amateur who knows either a lot about where they are or just enough about a variety of things to get a rough date, say plus or minus a few decades. An example of the last option would be if you got a quiz junkie who happens to have memorised the line of the kings of half a dozen or so ancient nations that their quiz master likes to throw at them like Rome, Classical Greece, Assyria, Babylon, and Egypt. That would mean that once they know who's in charge where they've got a smallish overlap period to work with.
Where is a lot harder, from what we have been able to piece together language and architectural styles didn't vary all that much across the region at that time, but the place names should help.
She knows Ramesses II.
The pharaoh Ramesses II was active in Egypt around 1200 BCE. Many of the buildings and statues built in his reign would still be maintained and good looking, and the locals could tell you about how long ago these things had gone up. Your Londoner heroine is familiar with these materials from the exhibits in the British Museum, which were acquired in the late 1800s and were still a big deal when your character was growing up. She in fact visited the museum while in high school and wrote an essay on Ramesses. She recognizes his statue and pieces together approximately when she is.
It all depends on how knowledgeable this person is. Please keep in mind that in 1920 England knowledge was not as readily available as today.
She is an ignorant layperson. "Ignorant" meaning she has no knowledge about ancient religions, languages, art and history beyond what's taught in grammar school. In that case, she may never find out that she actually traveled back in time and think that it may be some alt-Earth;
She is a well-informed layperson. She should be able to make a connection using names of the places, kings or architecture. However, it would be only a ballpark estimate and it may take a while for her to make such connection.
She has sufficient professional knowledge. She can be a history professor or an astronomer. In both cases it wouldn't be hard for her to pinpoint her position, both time and place, in a short while.
Dependant on her knowledge base entirely. L. Dutch's link in the comments is golden as far as the practicalities are concerned. By the stars is the standard answer up to a point. An ordinary person without specialized knowledge might not ever figure it out.
- Landmarks or rivers.
- Names of places. Only if she knows the Greek term for the area "land between the rivers" One way around this is to have her remember something from an exhibition, like the major cities in Phoenicia were Tyre and Sidon...for instance. Can be any small factoid that she can seize on.
- Art styles. If she's an ordinary person, she might not have a knowledge base, but might recognize vaguely that it's from ancient times. Ancient Assyrian art is super distinctive. While she might not be able to place where and when she is exactly, this will help.
- Languages spoken. This is a huge narrative hurdle, actually. If she can't speak the language it's going to be hard for her to even communicate. But if she has studied ancient languages or recognizes the use of a term that has fallen out of use, that might help.
- Technology. The Abacus. Unfortunately, this won't narrow things down, as the abacus has been in use since 3000 BCE. But by 1000 BCE in this area it will be everywhere.
- She saw it in a museum or in an illustration. Stealing from WillK's comment on his own answer. Beforehand, she sees part of a landmark or statue in the British Museum that's from Syria or where ever specifically she might be. The date was on the exhibition, and when she goes back in time, she sees it being built or unfinished.
ok, she is a reasonably sophisticated early 20th century britisher.
as a non-noble, and as a woman, her freedom of movement will likely be somewhat limited, she will likely need to be observational where she finds herself.
she should be able to recognize from architecture, clothing, artifacts & inscriptions/writing that she is in the ME, likely somewhere in the assyrian or babylonian empires. the use of cunieform writing puts the timing later rather than earlier in mesopotamian history.
if she knows her rulers, that will clinch the empire & era. the architecture between those two empires is distinctive, as well.
the fact that there are no hittites around lets her know its later than 1200 BCE. the presence of iron tools will reinforce the period.
the fact that there are no greeks or romans around lets her know it is earlier than 350 BCE.
this is also the age of the sea peoples (1200-900 BCE) raiding upon the peoples of the eastern mediterranean, so any references to them will peg the time to within a century or so.
given a cursory cultural knowledge, she can probably ascertain she is in assyria or babylonia or a minor kingdom within a few hundred years of uncertainty, absolutely depending upon her grasp of history, archaelogy, geography, architecture, linguistics.
I think she locate herself fairly simply with nothing more complex than a few star observations. The Earth's procession will have shifted our 'pole star' backward a bit from the 20th century Polaris partway back to Alpha Draconis. Knowing that the procession takes about 26,000 years, she can easily deduce ( as a measurement of degrees in procession) that she is well in the past , but not as far as a 120 degree offset , each 120 degrees being equal to about 8500 years.
Cornell Link She can also determine her physical location through a similar means, locate the pole in the night sky, determine the degrees from 90, and she has her latitude. Longitude is more challenging, but the remaining clues should be found in the trade and industries known for the time and culture.
Now she walks westwards until she reaches the mediterranean sea. She counts the days she needs, so she knows approximate latitude.
walking southwards along the coast will bring her to the remainders of the (united) kingdom of israel (Kingdom of Israel/Kingdom of Judah).
If she knows what Anno Mundi are, she just has to find some hebrew calendar/artifact with date inscription (in temple?) there to determine the time.
Apologies for the pre-edit version of this answer. I must have gotten the criteria for this question confused with one of the similar linked questions. The pre-edit version has lots more information that is usable if she is allowed to bring gear with her in preparation. Check the edit history if you are interested.
For "where", half of that is answered extremely easily.
You can estimate your latitude roughly just by looking at the stars, even without any tools. In your case, the destination is in the northern hemisphere which makes this even easier.
Just check the night sky on a clear night and look for Polaris, the North Star. It is directly over the true north pole, so it is pointing true north (true as opposed to magnetic north).
The angle of Polaris from the horizon, in degrees, is the same number of degrees latitude that you are on the planet. Someone even just half decent at this should be able to estimate their latitude to within about 5 or 10 degrees. That is an accuracy of a few hundred miles.
If you want a more precise measurement, you can make your own quadrant. They are so simple that you can find instructions online about how to make them out of paper. In this situation, you would be more likely to try and make a disk out of wood or clay. Then make markings on it to help you measure degrees; you can use some basic geometry skills to mark out 90 degrees and to continually subdivide that further and further.
You could also use plants (vines, sticks, tall grass, ...) to set up a measurement system, again using some geometry and/or trigonometry.
Either way, measure the angle up to Polaris again to get a better estimate of your latitude. If you can measure with accuracy better than a full degree, then you can estimate your latitude to within a few tens of miles, or maybe even a few miles if your measurement was good enough.
Hopefully you are either really good at geography so you have a mental picture of the world and where this puts you. If not, did you happen to have your passport with you?
This gets your position in a north-south direction. Along that axis, it is enough for you to realize you are in Mesopotamia. But that leaves out the east-west portion, so you could just as easily be in China or the Americas. But since your person is a history buff, hopefully they can tell the difference between the different cultures when they stumble into a city.