There are some highly upvoted answers here already, but I don't feel they've addressed the misunderstanding directly enough:
do you do this every level and have that many prepared spells to choose from each level?
No, you do not. As a druid, you can prepare spells (or change your list of prepared spells) every time you finish a long rest. The number of spells you can prepare is equal to your druid level plus your Wisdom modifier, and you can choose from the entire druid spell list, provided you only choose spells of levels that you have spell slots for.
This is different to, say, a sorcerer, who gains spells each time they level up. A sorcerer never prepares spells; they learn them when they level up, and can then always cast them. A druid never learns spells, they prepare them after a long rest, and can then cast those spells until they prepare a different set the next time they rest.
So, if you're a level 7 druid with a Wisdom modifier of +3, you can prepare 10 spells. This means that each time you finish a long rest, you pick 10 spells (of 4th level or lower, because that's what you have slots for) and those are your spells for the day. The next time you finish a long rest, you can, if you wish, wipe away that list of 10, and pick a new set of 10 spells (which can include some of the same ones as before, if you want).
When you gain a level, you become an 8th-level druid with a Wisdom modifier of +3, so now you can prepare 11 spells. Same as before, but now you can choose 11 spells instead of 10 each time you finish a long rest. Now, at 8th level you get an Ability Score Improvement, so you might add to your Wisdom, so that your modifier becomes +4. That would allow you to prepare 12 spells. Again, exactly the same, but now when you finish a long rest, you can select 12 spells to have as your spells for the day.
When you level up again, you're now a 9th-level druid with a Wisdom modifier of +4, which means you can prepare 13 spells, and you now have a 5th-level spell slot, so the spells you choose can be up to 5th level.
Types of spellcaster
Clerics, druids, and paladins have access to their entire class spell list, and prepare spells after a long rest. Bards, sorcerers, rangers, and warlocks learn spells when they level up, and then have that fixed list until their next level. Wizards are kind of in between, in that they add spells to their spellbook each time they level up, but they prepare spells from their book each time they finish a long rest. Do check how a classes spells work when building your character.