D&D TL;DR

- Dice notation is XdY; X represents the number of dice, and Y represents the type of dice. 1d6 is one 6-sided die.

- Every character has 6 stats: Strength, Dexterity ("Dex"), Constitution (health/defense), Intelligence (book smarts), Wisdom (street smarts), and Charisma (force of will/character and social skills). Constitution also affects your health.

- Your stats have both "scores" and "bonuses". The score is on a scale of 1 to 20 (for normal characters); 10 is neutral, and represents when you're average at something. A score of 0 means you have a bonus of -5, and for every 2 above 0 your score is, you add 1 to your bonus.

- "Proficiency" means that you're exceptionally good at something. When you're Proficient with something, you add your Proficiency Bonus to it. Your Proficiency Bonus increases with your level. You can be Proficient with Skills, Weapons, Tools, and saving Throws. In the case of Shields and Armor, being Proficient with them instead means that you're able to use Shields or that type of Armor.

- When you roll to determine whether or not you're successful in something (completing a task, hitting your attack, or evading an effect), then you roll 1d20, and add the related bonuses. Most weapon attacks use Strength, for example, so you'd add your Strength bonus. If you have Proficiency, you'd add your Proficiency bonus as well.

- When you roll to see if you succeed in something, there are two types of numbers you can roll against: DC and AC. DC (Difficulty Check) is for skills and saving throws (rolls made to avoid things); AC is Armor Class, and represents how difficult it is to hit or damage an opponent.

- Your character has a Class, Race, and Background (sorted in order of impact on your character). These can grant you abilities, stats, and Proficiencies. Some classes can also give you the ability to cast *spells.*

- Roleplaying! It's really important! It's really fun! Do it!

- If you're not interested in spellcasting, this is where you stop reading. The spells your character can learn (if any) are determined by both Class and level, of both character and spell.

- Spells have levels (0-9), which are effectively impact ratings. Level 0 spells ("Cantrips") are free to cast. Spellcasting Classes use Spell Slots in order to cast Spells. Spell Slots have levels attached to them, and the quantity of Spell Slots of each level you have increases with the player's level. There's no easy formula or anything for this-- you'll have to use the table.

- Spells of level 1 or higher can be cast with Spell Slots of higher levels (I don't know if there's a term for it, but I call it "upcasting"). Upcasted spells will, typically, have more impact than if cast normally, using the minimum required Spell Slot.