I often try to answer questions about how seeds work, and there have been several requests for a guide recently, so I thought I'd do my best to write one.
I'm going to be fairly comprehensive, but I'll try to keep the good stuff near the top, so don't think you need to read this whole essay to save or use game seeds.
==== A Guide to Using Seeds ====
How do I enter a seed?
For a seed that matches the DLC you own, create a new game, and change the settings mentioned by the poster, leaving everything else on the default. Then change any "don't matter" settings you like, such as difficulty level. Under "advanced settings", enter the game and map seeds.
If the game involves less DLC than you own, first disable any DLCs that the poster didn't have.
Can I change the difficulty?
Yes, you can change difficulty, game speed, disaster intensity, allowed victory conditions, and whether barbarians/tribal villages are enabled, without affecting the map or your starting position. You can also enable/disable most "game modes", but not Apocalypse Mode (the map changes fundamentally) and not always Secret Societies (the map and the opposing civilizations will stay the same, but in some cases you'll be given a different start location).
Can I change the leader/civilization?
Sometimes you can get the same start as another leader, and sometimes you can't.
Some civilizations (about half) have a start bias) to help them make use of their unique abilities. You can often switch between no-start-bias civilizations and get the same start (your choice may affect the set of randomly chosen civilizations, which could bump you to another spot in some cases).
You may sometimes be able to switch between civilizations with similar start biases, but many starts with civilizations that have a start bias will be unique to that civilization, or a very small number of similar civilizations.
It does not seem to matter whether you pick a leader directly, or receive the same leader randomly.
==== A Guide to Posting Seeds ====
Where can I find the seeds for my game?
On PC/Mac, press ESC to bring up the in-game pause screen. At the bottom, the game version number will be listed. Hover over it, and a pop-up will show the map and game seeds. The same can also be done on iOS, the menu is accessed from a button in the top right, next to the Civlopedia.
On all platforms, the seed being used for a particular game can be seen under "advanced settings" before starting a game; if you want to be able to share seeds for other platforms, consider taking a screenshot of the map/game seeds before starting your game, as I'm not aware of a way to check the seed after starting a game on other platforms.
If you're able to install mods, you can also install this mod to help identify not only your game and map seeds, but also what settings you chose when you created your game.
What settings should I post?
Post your installed/enabled DLCs and any settings that you changed from the default, but feel free to leave out difficulty or other "don't matter" settings.
What settings matter?
For a map: Ruleset, DLCs, map type, size, and apocalypse mode on the basic settings screen; resources, world age, temperature, rainfall, and sea level, if the advanced settings were tweaked.
For a start/game: all the settings that matter for a map, plus starting leader and whether 'secret societies' was selected; if advanced settings were tweaked, also the number of civilizations (and any non-random civilizations), number of city-states, start era, start position, and whether duplicate civilizations/leaders are allowed.
Game version could sometimes matter...but so far I'm not aware of a case where a patch affected peoples ability to reproduce seeds, as Firaxis have been careful to only introduce changes that affect the map in new DLCs.
What settings don't matter?
Feel free to change the difficulty, game speed, disaster intensity, allowed victory conditions, and whether barbarians/tribal villages are enabled. Most "game modes" can be freely enabled/disabled (with the exceptions of "apocalypse mode" and "secret societies").
==== Understanding Seeds ===
What is a seed?
Computers can't produce truly random numbers...so we use complex math that produces sequences of numbers that have the properties of random numbers that we care about. Since the numbers aren't really random, if you set up a pseudo-random number generator (RNG) the same way, you get the same sequence of seemingly random numbers out of it.
A seed is the value we used to set up the RNG...for the same program, using the same seed will result in that program making the same sequence of "random" decisions, so we can generate the same map if we use the same game settings and the same map seed, with the same version of the game...with the same game seed, we can generate the same set of random civilizations, and, if the map seed is also the same, the same start for each civilization.
Are seeds version-specific?
It depends on whether all major changes that affect map generation and starts are made by adding new DLC or game mode. The June 2020 update doesn't seem to have changed many seeds, if any, so I'm cautiously optimistic, but I'd still consider making a savegame for a start I might want to play, but may not get around to until after a new patch.
As noted above, for the result to be the same, both the seed and the program have to be the same...it's not enough for the random numbers to be the same, the meaning of those numbers has to also be the same...if we add just one additional decision that has to be made early, then each following number in the sequence applies to a different decision than in the previous version of the program, so the map that results will be radically different.
That's why seeds have a tendency to be version-specific in most games...any change to the game tends to change how many random decisions have to be made, which changes the meaning of a seed.
In the Civilization series, changes are often made by adding a new (sometimes free) DLC, or a new game mode, that can be turned on or off, so there is some hope that older seeds may continue to work, if you configure your game by turning off any newer DLC.
It appears the June 2020 patch did not affect game seeds, or affected very few. (It's possible a few Gathering Storm starts could differ because of the increased yields added to several underpowered natural wonders, but I'm not aware of one that does.)
It is still possible a future patch could make older seeds impossible to recreate, however. If you see a seed that you want to play later, but not quite yet, consider making a save-game at your preferred difficulty now, so you'll still have access to that start if a major patch makes older seeds impossible to recreate.
Are seeds cross-platform?
Seeds are cross-platform between Windows, Mac, and Linux (with occasional brief exceptions when a new expansion hasn't made it to Mac or Linux yet). At least one Switch player was able to recreate a PC seed, so there's a good chance that console versions are also compatible, when the DLC matches.
However, at present, I'm fairly sure that all-DLC seeds are not cross-platform between PC and at least some console versions, because not all minor DLCs have been released on every platform.
Do mods affect seeds?
Mods that add civilizations, luxuries, resources, or natural wonders do, and should be considered the same as DLC - list them alongside your DLC when posting seeds that require them, and disable them when using a seed that doesn't require them.
UI-only mods (like Sukritact's simple UI adjustments, or the seeds and settings UI mod linked above) don't, can be used without affecting a seed, and don't have to be mentioned when you post a seed. Mods that only affect game rules, such as historic speed, should also work.
If you want to play a particular start with a modded civilization, there's a some chance you can enable just that one mod and do so, as long as it doesn't come along with new resources or natural wonders (which would change the map), and its start bias doesn't cause you to start in a different location (see also "Can I change the leader/civilization" above).
