Unit shards are the things let you limit break your unit so they can reach level 99 and job level 15. You can get them as rewards from summoning, or getting duplicates of a unit that you already have, but you need a total of 600 unit shards to fully limit break a unit, which can be quite costly if you are solely relying on summons.
If you plan to EX awaken your unit, then you need another +400 (1000 total) unit shards to get max EX job level.
If you just got the newly released character(s) on a banner, then the game provides several ways to help get their shards.
The first one is the unit missions, that you can get to by selecting it from the home screen.
In total, you can get 120 shards by completing all of them. The missions simply require you to level up the character and main job's level. Though, in order to complete all the missions and get all the shards, you do need to have the unit at limit break 3 to reach level 75, which is 240 shards.
The shop always offers some unit shards daily, including the currently on going banner characters and some random ones, so it's recommended to check the shop daily.
You can refresh the main shop by tapping on the "update" button on the bottom right. It can be updated several times a day, and the first one each day is free, but will cost some visiore if you want to reset again on the same day.
The shop also has different banners that you can check out. New characters always have their own shop banner section where you can buy a total of 120 shards by using 6000 free visiores.
Other shop banners sells unit and vision card shards as well, so be sure to check out all the shops in case shards of units that you are currently trying to build is there or not.
Mog shop is where you use medals that you obtain from various sources like summons, arena, guild, or friend medals, and they also refresh daily.
When you summon on a banner, you will get a certain "month" medal. Each summon gets you 10 medals, so 2 summons is essentially 1 extra unit shard that you can get. These monthly medals have a time limit, so be sure to use them up before they expire. The character banner mog shop have 600 shards, which is enough to fully limit break a unit.
Friend and Guild Medals
Both Friend and Guild Medals offers some specific units and unit shards. These options change once in a while, but they stay with the same set for a while after the change. This can be a good and consistent way to get new units and build them up.
You get friend medals from people in your friend list that sends you gifts based on your desired gift option, as shown on the left side of the friend screen. You can choose to set it as other options, but the medals are the valuable ones. Tap the "Gifts" button in the friend screen to claim and send some gifts to people in your friend list.
Getting guild medals works similarly, except you need to join a guild in order to send and receive. Getting medals from guild is only one of many benefits that it offers, so it's highly recommended to join a guild as soon as possible if you're a new player.
Soul and Vision Medals
You can get unit soul medals once you get more unit shards past 600. The soul medals can be exchanged in the mog shop for various unit shards. It doesn't have all units, but the shards that you can buy aren't limited. If you happen to whale on the game and get a lot of excess soul shards, you can use them all up to fully limit break old units that are available.
Whimsy shop is a shop that can occasionally show up once you finish certain quests. Once the shop is open, you can go to it by tapping on the Whimsy shop button on the bottom side of the game's home screen. Once you open the shop, it will only be available for 30 minutes. After it closes, you will have to wait a certain amount of time before you can try to get it back again.
If the shards that you are looking for aren't in the shop, or don't want to spend any visiores, shard quests are another way of getting specific unit shards.
With the exception of some collab, or limited time units, most units have their own shard quest. Completing the quest gives you 1 shard, and the amount of times you can do a specific quest depends on the unit's rarity. UR units have a limit of only twice per day, while MR units are limited to 3 per day. You get 10 attempts per day, which means you can try to go for 5 different UR units.
If you are solely relying on this feature, then this process can take a while to fully limit break a unit from 0 shards. However, it's a free way of obtaining them, and doing this every day can help speed up the process and potentially makes it so that you only need less duplicates from summons to get max LB.
Chocobo expeditions has a chance to give you a UR unit shard as well. However, you can only get shards of the same element unit as the destination of the expedition. Going for a green magicite expedition gives a chance to get unit shards that are wind element, such as Ayaka as shown above.
This one is more of a longshot, but it won't hurt to do if you don't need to get a specific elemental magicite. You can also increase the chance of getting rare items by using units that give increased rates. Tap the "unit bonus" button in the expedition destination screen to see what the currently boosted units are.
Similar to the Whimsy shop, occasionally after finishing a quest, there is a chance to get a chocobo expedition bonus that will last for about an hour. During this time, rare item drop rates are increased, so this could be a good opportunity to use up your expedition tickets for a higher chance at getting some shards.
Some events also utilizes the chocobo expeditions through increased rates, or in this example, a new time limited expedition area entirely. The rewards can be random, so it won't help if you need specific element magicites for your esper(s), but it's still best to take full advantage of these event areas, otherwise, the only way to get collab character shards is through the barracks.
The guild barracks can give unit shards after the anniversary update. We have the option of choosing between going for unit shards, or get Job Points. The time it takes to give a unit shard is based on a unit's rarity. UR units takes 12 hours to get 1 shard, MR or below takes 8 hours.
Collab units in the barracks gives collab medals instead of specific unit mindspheres past the 600 shards. This is useful if you have multiple collab units and want to focus on only 1 of them by putting both to get double the rate.
"[...]Going for a green magicite expedition gives a chance to get unit shards that are earth element, such as Ayaka as shown above[...]
=> wind element