Genshin Impact is great fun, but make no mistake: this is a gacha game. It is designed specifically to suck away time and money from you, and one of the ways the game does this is by offering a drip-feed of currencies you will feel compelled to collect and spend in the optimal way.
See below for the most important currencies Genshin Impact offers, how to collect them, and what you should spend them on. This guide is a resource for early game players to know what they're in for in terms of grind, as well as what they should hold onto heading into the late game.
What are they: The first and most obvious currency in Genshin Impact is Primogems. These little guys can be used buy Original Resin (i.e. stamina for bosses and domains) or Fates, which allow you to wish for new characters and weapons using the game's virtual slot machine.
How to get them: You can get Primogems from doing just about anything: completing quests, opening chests, discovering teleport waypoints, filling in your Adventurer's Handbook, completing Spiral Abyss floors, unlocking achievements, the list goes on and on. In most cases, you only get a smattering of Primogems as a reward. This is because they are perhaps the most saught after currency in the game and the developers at miHoYo would much rather you lose patience and buy some than grind them out without paying.
How to spend them: Whether you care about the gacha part of Genshin Impact or not, you should absolutely save your Primogems to pull for characters. The game is designed such that you can only make significant progress in tough areas like the Spiral Abyss with a diverse cast of strong adventurers. There are good weapons you can craft instead of wish for, and you can just wait for your resin to replenish, but you can't get a five-star character unless you feed that slot machine, baby.
What are they: Fates are the individual items you earn or buy (with Primogems) to use Genshin Impact's slot machine. There are two kinds--Acquaint and Intertwined--which essentially operate the same way, though they dictate which "banner" you can use them on (note: a "banner" is common terminology in gacha games to refer to the rotating types of virtual slot machines that come and go from the game).
How to get them: The most common way to get Fates is to spend Primogems on them. Both Fates cost 160 Primogems each. You also occasionally get Fates as a reward for increasing your Adventure Rank. The only other way you can get Fates is to purchase them from the Starglitter and Stardust Exchanges, which are explained in more detail below.
How to spend them: As mentioned above, you want to spend Fates on pulling characters. You have the option to spend a single Fate at a time or do a bulk Wish of ten. There is no particular benefit to saving Fates and spending them in bulk, though I suppose getting ten rewards at once (including at least one guaranteed four-star pull) is probably more satisfying than single pulls. If you really want to min/max your rewards, though, you should stick to single pulls, as you can save Fates after triggering the effect that gives you a four-star item or Adventurer.
What are they: Original Resin is essentially a stamina meter that limits how much you can repeat certain dungeons and boss fights, most of which provide valuable materials for leveling up your Adventurers and their gear.
How to get them: Original Resin replenishes automatically at a rate of one every eight minutes. You can't just bank Original Resin indefinitely, though. You can only have a maximum of 120 Original Resin at once, so managing this meter so you're always accumulating is important for making efficient progress in Genshin Impact. If you run out of Original Resin, you can also spend Primogems or Fragile Resin to replenish your meter. As mentioned previously, you shouldn't spend Primogems like this, but Fragile Resin (which you can get as quest rewards) is fair game if you want to top up your resin meter.
How to spend them: This kind of depends on what characters you have and what they need to continue going up their upgrade treadmill. You certainly have some freedom here, as you'll always earn your resin back, but to maximize efficiency, you should probably take on the hardest quests possible (using co-op partners if you need help) to get the best possible rewards.
What are they: Mora is the currency actually used by the people of Teyvat, and you use it on virtually everything. You spend Mora to buy items, craft things, level your Adventurers, and enhance gear. The further you progress in Genshin Impact, the more important Mora, and lots of it, becomes.
How to get them: Mora drops off of nearly everything in Genshin Impact, but there are more efficient ways of getting it than others. Solving puzzles, opening chests, and completing quests generally grant more Mora than simply killing random enemies. You can also buy Mora using Sigils and other currency (more on that later).
How to spend them: Mora is something that will seem like an infinite resource in the early-goings of Genshin Impact, but it becomes one of the biggest bottlenecks in the later stages of the game. Make sure you focus your investments on a core team of Adventurers that work well together and gear that plays to their strengths. Otherwise, try to avoid spending Mora on materials or anything else besides character and weapon enhancements for your core team.
What are they: Starglitter is a special currency that can only be spent in a specific tab of the in-game store. It is a sort of consolation currency that can be saved up to buy some pretty sweet rewards.
How to get them: I call Starglitter a pity currency because you earn it whenever you use Genshin Impact's virtual slot machine and receive a character you already own. Each duplicate character pull gives you a few of these items, and that's the only way to earn it.
How to spend them: There is only one place to spend Starglitter: The Starglitter Exchange. This is a storefront that lets you purchase Fates in limited quantities and even specific characters. The catch here is that you need quite a bit of Starglitter to purchase any of these items. In general, I'd recommend holding onto your Starglitter to buy characters that you really want (provided they become available).
What are they: Stardust is basically the same thing as Starglitter, but you earn it differently and spend it on a different storefront.
How to get them: Duplicate weapon pulls grant Stardust just like duplicate characters grant Starglitter. This is the only way to get Stardust.
What to spend them on: There is also a Stardust Exchange that has similar items to that of the Starglitter Exchange. You can't buy characters here, but you can buy Fates. Make sure you do that. You can also buy Mora here, which is useful in case you're running low. I wouldn't spend Stardust on anything else in the store, though.
Anemo and Geo Sigils
What are they: Sigils are a resource you can spend in the Souvenir Shop in either Mondstadt or Liyue. Each location only accepts sigils from their governing element though, so you can only spend Anemo Sigils in Mondstadt and Geo Sigils in Liyue.
How to get them: You earn Sigils from opening chests, sending adventurers on expeditions, ranking up Statues of the Seven, and sometimes just by investigating items around the world of Genshin Impact.
What to spend them on: The Souvenir Shop sell all kinds of materials that you can either craft or farm, with the exception of Memories, which you can use to advance the constellation on the Traveler Adventurer. Unless the Traveler is a core member of your Adventure team, you should only spend Sigils on Mora. Sigils are somewhat farmable though, so it's not dire if you decide to spend them on something else to speed up your progression.