At Adventure Rank 45, you are now able to do the highest difficulty artifact domains. In the highest difficulty, you are guaranteed to get one 5 star artifact per run, and this is the biggest benefit of reaching AR 45.
You can use condensed resin to get double the drop rate to speed up the process. If you only just reached AR45 and find these high level domains difficult, then you can do them in co-op with friends or random people.
You can farm certain artifacts by defeating Elite Enemies that's roaming around the map. Elite Enemies spawns daily, and they are always at the same location. There are certain places with clusters of enemies that can be a convenient place to visit daily.
If you want to get some free artifact exp fodders, you can also visit certain locations that drops low level artifacts. Similar to the elite enemies farm, you can do these daily because they respawn every 24 hours, based on when you picked them up, instead of server reset.
It's recommended that you ascend your party to level 80, or at the very least, just your 2 main DPS, because you need 2 teams for abyss. You will get some bonus stats when you ascend your character, and more stats when you feed them +10 levels. While it may not seem like a big stat increase, increasing your level is actually pretty important. This is because the damage that you deal gets lower if you are attacking a monster with a higher level than you, which is part of the game's damage calculation. Naturally, you will also deal more damage if you are attacking enemies that are lower level. This is arguably the first thing that you should do before artifact farming since it will help make things more easier, and less of a gamble with your resin.
Clearing Abyss 12
Since you can already farm for 5 star artifacts from domains, you can essentially equip your team with the best gears. This means that you should be able to tackle the current hardest content in the game, which is floor 12 of abyss. Floor 12 can be quite challenging and a big DPS check, so it requires proper setup and gears. You may not be able to clear it as soon as you reach AR 45, but you can make this the goal that you should aim towards.
Abyss floor 9 ~ 12 resets every 2 weeks, so if you don't do them, then you are missing out on some free Primogems, and some free 5 star artifacts from the reward boxes when you complete a floor.
This is just an example stats that you should be at for your main DPS. It's taken from a Diluc with fire resonance, and using Prototype Aminus (which has atk% secondary so it's a little inflated). The artifacts are mostly 4 stars except the feather, only the hourglass is using atk% mainstat, cup is elemental damage%, and hat is crit rate. With a full 5 stars set, you should be at around 2,000 attack. Try to aim for around that number if you want to clear floor 12.
Preparation for next ascension
If you are feeling unsure on what to use your resin for, then you can't go wrong with farming the materials required for your team's (or just main DPS) next ascension. You need 6 of the 5 star elemental stones, and 20 of the boss drops.
Each kill of a boss only gives you 2/3 of the boss item, this means that you essentially need to run them a minimum amount of 10 times, which is 400 Original Resin. This is (400x8/60) 53.3 hours or 3 days worth of resin, just to ascend 1 character, assuming that you only got 2 each attempt. If you get 3 per run, then you only need 7 runs, which is (7x40x8/60) 37.3 hours worth of resin. Unfortunately, it's still going to take more runs than that, because the 5 star elemental stones don't drop like the other material. Many players have said that farming for enough boss materials is still not enough to get 6 of the elemental stones.
If you only start farming for these when you reach AR 50 and increased your world level, you will end up setting yourself back by potentially weeks, and things will be even more difficult because enemies' levels have gone up. Make sure to also stock up on some Mora and exp books so you can actually level them up after ascending them. It takes 171 Hero's Wit + 3 Wanderer's Advice to level a level 80 character all the way to 90.
Hopefully you didn't forget about the weapon(s). Though, this one is less taxing on your resin, but more on your Mora and Enhancement Ores. It takes over 250 Mystical Enhancement Ores just to level up a lvl 80 weapon to 90.
Not exclusive to AR45, but there are a handful of things to do every day. The daily stuff are commissions, mining, and maybe even elite enemies farm. Then there are still plenty of weekly missions like the ones from city reputation, and BP missions. Occasionally, there are events to do as well, that you can check by pressing F5 (on pc).
If you haven't finished it already, it's recommended to complete both of the towers to max level. This increases your maximum stamina, and gives some Adventurer's Exp as well. Doing this can help prepare you for the next content when it's available.
Just an optional thing to do, since there is nothing to gain from by getting 100% in all areas. But picking up treasure chests can be a good way to get Anemo/Geo sigils. These are used to exchange for items some items and Mora at the gift shop, available in Mondstadt and Liyue Harbor. The items that you can buy are limited, but the Mora is not.