You should save your mana prisms for November when Chaldea Teatime comes out. 1000 mana prisms a copy (5000 mana prisms total to MLB).
Similarly, if you got the rare prisms to unlock them in the Shop you should get Chaldea Lunch time and most importantly Mona Lisa as well. They each costs 1 rare prism to unlock each of these and then 1000 mana prisms per copy (again 5000 mana prisms total to MLB).
As for how to gain them the best way to get them is through events. When an event comes along they almost always give out 1000 mana prisms through either the shop or through the event rewards. And usually there are 1-2 events per month.
After that do the 40 AP dailies ONCE a day. The 40 AP Dailies give 4 mana prism for the first clear.
After that, and only if you don’t need them to raise any servants, burn any and all silver embers. They convert into 1 mana prism each. DO NOT BURN gold embers as they give 3 x as much exp as the silver but only 1 mana prism. Just not a good trade off.
Similarly burn all duplicates of silver or gold servants you have that are np 5. You could burn them before then if you never use them but almost every servant has a niche use and you probably are better to get them to np 5 then burn all the duplicates after that.
Now here is where it gets tricky.
If you need QP you shouldn’t do this step im about to describe. If QP isn’t an issue then repeatedly run the 30 AP Embers node. You get 3 mana prisms on the first clear but that isn’t why you should run it. You run it REPEATEDLY cause it mainly gives silver embers. Burn the silver embers to get mana prisms. THIS IS THE BEST WAY TO GET MANA PRISMS OUTSIDE OF EVENTS. However, it is AP inefficient and if you need QP you should run doors instead.
Doing the 40 AP nodes once and then doing nothing but spam running the 30 AP node will net you about 51 mana prisms a day. Over the course of a month that is 1,530ish mana prisms.
BUT AGAIN IF YOU NEED QP DO DOORS INSTEAD. Even if you are getting Mana prisms for the Mona Lisa it is overall more QP in the long run to do doors instead!
Hope that helps!