Saint Quartz is the premium resource of Fate/Grand Order. Its uses are as follows:
Summon new Servants and Craft Essences that range from 3 Star to 5 Star. This costs 3 Quartzes per pull, and you can simultaneously pull 10 times (this costs 30 Quartzes). An alternative of this is using the Summon Ticket, and you can only use single pull with it.
Gain 100% of your Maximum AP. This costs 1 Quartz, the alternative is to use the Golden Apple item.
In battle, when your whole party has been wiped out, you can use 1 Quartz to resurrect your whole team with maxed out NP. The alternative of this is using three Command Spells at once
How to Get Quartz?
Buy it with money
Go to the Da Vinci Shop and pay real money to get Quartzes. You will get several Quartzes and some bonus free Quartzes.
While this is not recommended for those preferring 'Free To Play' style, there are several Summoning Banners that require you to use Free Quartzes. These banners are the ones where you are guaranteed to get 1 SSR Servant, but you can only summon ONCE.
Daily Login
Logging in daily will occasionally give you free Saint Quartzes. To do this, you have to log in consecutively every day, and depending on the number of the days, you will get a free Quartz.
In the second, fourth and sixth consecutive login, you will get 1, 1 and 2 Saint Quartzes respectively, and after reaching the seventh consecutive login, the login counter will reset to one. So if you login every day of the week, you will get 4 Saint Quartzes per week.
In addition, the game keeps a counter of how many times you logged in total, after a certain number, you will get a lot of Quartzes. The table below lets you know how many logins you need and how many Quartzes you will get.
Login times
Quartz received
10
4
20
4
30
4
40
4
50
4
75
10
100
20
Every 50 days after (150, 200, 250, and so on)
20
Completing Quests
Everytime you finish a Main or Free Quest in a Singularity, you will get 1 Saint Quartz. There are also some areas that only have Free Quest, so you will get that, while a certain area may have multiple Main Quests, you will still get Quartzes that way.
Events
Certain events sometimes offer Saint Quartz as rewards. Refer to the event pages for more details on this. However, remember that if the event is gone, the Saint Quartz reward is gone forever.
Exchanging Saint Quartz Fragments
Finishing Master Missions will grant you 2 Saint Quartz Fragments, and 7 of them can be combined into 1 Saint Quartz. There are seven Master Missions that refreshes every week, so if you complete them every week, you will get 2 Saint Quartzes per week.
Each Servants has Bond Levels. While the first 5 Levels unlock Bond dialogues, depending on their rarity, if you get their Bonds to Levels 6 to 9, you will be rewarded with Saint Quartz. The table below should help
Servant Rarity
Reward for Bond Level
6
7
8
9
5
x3
x3
x3
x3
4
x2
x2
x2
x2
3
x1
x1
x1
x1
2
x1
x1
x1
x1
1
x1
x1
x1
x1
Maintenance Compensation
Whenever a new patch is incoming, the game usually goes for a maintenance. When the phase is done, you will receive Saint Quartzes equal to how many hours did the maintenance take place.
There are other unexpected maintenances that may have nothing to do with updates for new contents, but either way, you still get that many Saint Quartzes.
Special Occasions
This only happens rarely for certain 'events' (not to be confused with in-game events), where the administrators decide to give you Quartzes.
Farming Quartzes
Based on the methods to get Quartzes above, the actions you need to do in order to farm Quartzes are:
Log in every day: 4 Quartzes.
Finish all Master Missions every weeks: 2 Quartzes
Use your favorite Servants and raise their Bond Points (this really depends on your roster)
With this, you can at least generate 6 Quartzes per week! And that's not including the Bond Point reward, the total login reward, and occasional maintenances.