Using the slot does not 'expend' nor 'consume' the spell
Note: This answer has quite a bit of the rules text cited with the intention of helping a new DM better translate the Players Handbook (PHB) text into a 'how to apply this in your game' since the game is being played by new players+new DM.
Spell Slots
Regardless of how many spells a caster knows or prepares, he or she
can cast only a limited number of spells before resting (PHB Chapter 10)
What you described as your understanding is how it worked in older editions of the game. In D&D 5th edition spell casting is more flexible.
A spell slot powers any known or prepared spell of its level.
You ask about the druid and the sorcerer. Their mechanics are slightly different. One is a prepared spells caster, one is a known spells caster.
Known and Prepared Spells
Before a spellcaster can use a spell, he or she must have the spell
firmly fixed in mind...Members of a few classes have a limited list of spells they know that are always fixed in mind. {Sorcerers are one of those classes}.
Other spellcasters, such as clerics and wizards, {and druids} undergo
a process of preparing spells...In every case, the number of spells a caster can have fixed in mind at any given time depends on the character’s level. (PHB, CH 10)
Druids prepare spells, and sorcerers know spells. This is a mechanical game distinction. (Ch 10 PHB, Spellcasting, and CH 3 in the Spellcasting sections for Druid and for Sorcerer class descriptions).
Sorcerer: Spells Known of 1st Level and Higher
The Spells Known column of the Sorcerer table shows when you learn more sorcerer spells of your choice. Each of these spells must be of a level for which you have spell slots. For instance, when you reach 3rd level in this class, you can learn one new spell of 1st or 2nd level...when you gain a level in this class, you can choose one of the sorcerer spells you know and replace it with another spell from the sorcerer spell list, which also must be of a level for which you have spell slots. (PHB, CH 3, Sorcerer)
Druid: Preparing and Casting Spells
The Druid table shows how many spell slots you have to cast your druid spells of 1st level and higher. To cast one of these druid spells, you must expend a slot of the spell’s level or higher. You regain all expended spell slots when you finish a long rest.
You prepare the list of druid spells that are available for you to
cast, choosing from the druid spell list. When you do so, choose a
number of druid spells equal to your Wisdom modifier + your druid
level (minimum of one spell). The spells must be of a level for which
you have spell slots.
For example, if you are a 3rd-level druid, you have four 1st-level and two 2nd-level spell slots. With a Wisdom of 16, your list of prepared spells can include six spells of 1st or 2nd level, in any combination. Casting the spell doesn’t remove it from your list of prepared spells.
You can also change your list of prepared spells when you finish a
long rest. Preparing a new list of druid spells requires time spent in prayer and meditation: at least 1 minute per spell level for each
spell on your list. (PHB, Ch 3, Druid)
To address your questions one by one:
Each day players "prepare" list of spells for that day, and place one
in each spell slot to use later.
The Druid prepares, the Sorcerer does not.
Is this correct?
Not for this edition of the game. Any slot can be used to apply any known or prepared spell of the appropriate level.
Can each spell be used only once per day?
No. That is how it worked in AD&D, Basic D&D, in Original D&D, and in 3rd edition D&D. In this edition, that has changed. The character prepares or knows a number of spells of the same level, and any slot can be used to cast any spell of the appropriate level.
Examples:
- a level 1 Druid prepares both Entangle and Healing Word, and has
two spell slots at first level. The druid can cast Entangle twice,
or, Healing Word twice, or, each one once - before running out of spell slots for that adventuring day.
- A sorcerer has chosen Sleep and Magic Missile at first level and has two spell slots at first level. They can cast Sleep twice, or, Magic Missile twice, or, each one once - before running out of slots for that adventuring day.
Do spells come from all spells for that level or only known spells?
That depends on the character's class.
- The Druid has to pick which ones to prepare after each long rest
from any spell on the list for their class and level.
- The Sorcerer, once a spell is known/chosen, always has it ready to
cast (Known spells is the in game term for this). They can only
change that after they increase in level.
If it comes from "known spells", how does a druid or sorcerer add to
their list of "known spells"?
The druid can prepare any spells from the druid list that their level allows them to cast.
The Sorcerer has to make a choice at character generation, and at each level up.
Example: a druid of level 2 with a Wisdom of 16 prepares their level + Wisdom Bonus spells each day at the completion of a long rest. They have the whole spell list to choose from, but must decide which five to choose. (They can always choose to have prepared what they had done ono the previous day). The bonus spells from their circle (Circle of the Land) are always prepared, and don't count against the above slot formula.
The Sorcerer at level 2 had two spells already known from level 1, chosen from the Sorcerer list. At level two, they get to pick one new spell that they already know, and can replace one of the previous ones that they knew - but perhaps they found that they don't like as much as they thought they would.
The spell slot, which recharges after a long rest, can be used for any of the spells with that same level.
Spell Slots (PHB, Ch 10)
When a character casts a spell, he or she expends a slot of that
spell’s level or higher, effectively “filling” a slot with the spell.
{snip}. So when Umara{a third level sorcerer for example} casts magic missile, a 1st-level spell, she spends one of her four 1st-level slots and has three remaining.
Note that the spell slot is what is expended, not the spell. The spell remains in the caster's mind; to cast it requires the slot.
Finishing a long rest restores any expended spell slots (see chapter 8
for the rules on resting)
