I apologize in advance, as I fully admit that this post is asking for the community to help me overcome some of my reading comprehension problems. However, with the success I have had with this community, I am very hopeful for the results in my 1 year study of the wizard class.
What gets me the most confused is how interwoven the terms spells known, prepared spells, and spell slots are used, which jumbles as I read it, so here's how I understand it:
Spellbook: a fancy notebook (tattoos or whatever that can contain notes written in expensive ink) that holds all the theoretical formulae regarding your studied spells.
Spells Known. The number of spells you have studied and have the formulae written down in your spellbook. This is equal to 6 at level one and increases by 2 for every level, BUT can also increase if you can borrow the notes from a spell scroll or another person's spellbook.
Prepared Spells: If the spells known would be the notes taken on each spell, I am guessing the prepared spells would be a quick guide for practical use. Kinda like having a mnemonic fresh in your head. The number of prepared spells, or mnemonics you can remember, are calculated by your Intelligence modifier + your wizard level, aka how smart you are plus your experience.
However, some spells do not require being prepared for practical use and can be done the long way, which is called ritual casting. So as long as you don't mind spending an hour to cast it, you could cheat and say your prepared spells are your Int Mod + Wiz Lvl + Known Rituals, so to speak.
Finally, Spell slots: The best way for me to understand how this works is by looking at this like a vending machine with a broken return slot. Your body produces a certain number of "spell slots" or coins per day, and you can use them to produce any spell you have prepared (ignoring the rituals you cast). While sometimes you can pay a bigger coin to get a bigger bottle of the spell, there is no way to make change, so you'll have to use whatever you got if you want to cast a spell.
If that is all correct, that would mean that you are reliant on the balance of all three to be a wizard, with little to no physical skills aside. So you stand in the back of people who can stab others and cash in your coins to help them out. Meanwhile how effective you can be is reliant on what spells you know how to cast and which one you remember well enough to cast immediately.
Have I finally understood how to play a wizard?
Best Answer
While this answer may not fully address all of your concerns:
Yes, you appear to have a basic understanding of the mechanics of playing a wizard. I've run tables with players with very young and reading deficient players before, and one thing I highly recommend for such players are index cards.
Create an index card for every spell known that you have, with the complete spell description and a "Cheat notation" of whatever your saving throw is or damage done at your current level written on it. Then just set those cards out in front of you that are "Prepared". You can use tokens or dice as markers to notate your daily uses, which you can remove or spin down as you cast your spells. You can also make personal notations of how and when to best use those spells to prevent over referencing and you can express those spells in your own words for simplicity.*
When you cast a spell, remove a token, or put the spin down a counter. And you're done. Daily spells and such taken care of with a sense of physicality that may help you keep track of everything.
Doing this will greatly help speed up play and take a lot of the work of guessing about what you can and can't do with your magic slots, letting you focus more on the game and not about what the explicit description of the spell is in the book. It will also let your more experienced comrades visually see what resources you have available and give advice for what you could be doing in a round until you get the hang of things.
Wizards of the Coast also published spell card decks that are essentially every spell for a class. But those can get expensive, and what's written on the cards may not be exactly what you need. It's a lot faster starting out to just make the few starting index cards for your spell list and go from there.
Best of luck.
=)
*Previously I had mentioned that you can remove cards to cast "Prepared" spells. This is a holdover from 3.5. With 5e, once a spell is prepared it is not "lost" once cast, you merely expend the appropriate spell slot for the day. I apologies for any confusion.