If you have to use a spell slot to put a spell into the ring of spell storing, do you again have to spend a slot to cast a spell from the ring?
No, someone already spent a spell slot (or slots) by filling up the slot(s) in the ring
Ring of Spell Storing Ring,
rare (requires attunement)
This ring stores spells cast into it, holding them until the attuned wearer uses them. The ring can store up to 5 levels worth of spells at a time. When found, it contains 1d6 − 1 levels of stored spells chosen by the GM. Any creature can cast a spell of 1st through 5th level into the ring by touching the ring as the spell is cast. (SRD, v5.1, p. 237)
I italicized "cast into it" and "as the spell is cast" as a link to basic rules on spell casting.
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. (Basic Rules, p. 82)
As an example: a Fighter (Champion) can cast a stored spell from this ring without even having spell slots from their class (they have no spell slots), once they are attuned to the ring that has spells already stored in it.
For what it's worth, we have a lot of related questions on the Ring of Spell storing. You may find them all of interest, since it's a very versatile item. My first D&D group applied this approach to provide familiars for multiple characters by using the ring.
To answer your comment:
So I can cast spells into it, then change my prepared spells and have a wider range of spells ready.
Yes, that is a way to use it (preparation). Think of it as a wallet. You put some cash into it and you can go and spend the cash while shopping. Then it's empty. You have to put some more cash into it to fill it up before the next shopping trip.