Soldier cards are the cards you use in the battle dungeon. There are 6 types of soldier card:
Above is an example of a soldier card profile
On the card itself in the top left, the icon at the bottom right of the card indicates its type (in this case, it's an attack type).
The bar at the bottom of the card picture in the top left is the card's "Loyalty". When you lose a mission with this card in your squad, the loyalty bar goes down. When it reaches 0, the soldier abandons the Shinsengumi and takes refuge in Mukurogai. Find the soldier there to convince him to rejoin the unit.
The top right shows its current level and max level as well as the experience required until it next levels up (cards you have in your squad in the battle dungeon gain experience after completing a mission)
Under that is "health" - the combined health of all the cards in your squad is given to you at the start of the mission as a bonus (for example, having just this card in your squad would give you 1670 bonus health at the start of the mission)
The number under that indicates the speed at which the cards gauge refills (after using its ability). The higher this is, the quicker the gauge refills and the sooner you can use that ability again
Both health and refill speed increase as the card levels up
Under that, there are sections describing both the soldier ability and corporal ability. The soldier ability is the normal ability for all cards. The corporal ability is the effect the card has when it is selected as the corporal of a squad. You can still use your corporal's soldier ability, but he also has the corporal ability active as a bonus.
There are different levels of the effects. For example, one attack card could have an effect boosting Ryoma's attack power by a "small" amount (a common attack card) whereas another could have an effect boosting attack by the "maximum" amount (super rare attack card). It's the same with other abilities such as refill time - "Maximum" increases refill time by the highest amount, "Small" increases it by the smallest amount.
There are 3 different types of weapons the soldiers have - "Sword", "Spear" and "Gun". You can see what weapon they have in their card picture.
When in squad organisation, the first slot of a squad is the corporal slot. The rest of the slots are regular soldier slots. When you select an empty slot, choose the first option to insert a card.
When you select a slot which already has a card, choose the first option to swap it with another card. Choose the second option to use the "synthesise" option - you can synthesise cards to increase the experience of the base card. Of course, you lose the cards you used to synthesise with the base card after doing this.