These are the famous words you'll hear right before combat begins in a game. Combat works in turns, meaning that every player and enemy has a turn to take actions. Once everyone has had a turn, the round is complete, and the turns reset.
Rounds are six seconds long, and turns are typically a second. So a combat session that lasts 10 turns would be exactly one minute long in real time. This is important to remember when casting spells that have time limits and duration!
Turn order, called "initiative," is determined by rolling a d20+your DEX modifier. Your DEX modifier will also be listed in the Initiative section of your character sheet. When player characters roll the same initiative, discuss amongst yourself who will move first. Typically, it will be the player with the higher DEX score, but it can also be discussed strategically amongst yourselves. If a player character rolls the same initiative as an enemy, typically the player will move first.
Combat works similarly to ability checks. Instead of rolling against a DC, however, you'll be rolling against a creature or character's AC, or Armor Class.
If the player's attack roll (a d20 plus whichever modifier their specific attack dictates) is equal to or higher than the AC of an opponent, it's a hit! The player will then roll the appropriate dice to deal damage to their opponent.
Fun fact: Dungeon Masters keep their own house rules about Natural 20's and Crit 1's in combat. When a player roll a Natural 20 on a hit, the damage can be doubled or rolled twice, depending on the DM's rules. A Crit 1 will always miss, however, and will sometimes have negative consequences for the player, such as getting disarmed or falling and becoming prone.
In 5e, there are two kinds of magic: spells and cantrips. Cantrips are magic spells that the character has learned over time and they know these spells so well that they are innate. Cantrips can be used as many times as needed without expending any resources such as components or spell slots. Both cantrips and spells are categorized by different schools of magic such as Transmutation or Illusion. Each class can only learn certain schools of magic, so pay careful attention!
Spells are learned by the character either through experience, studied from a book or scroll, or from being taught by a tutor before or during their journey. Spells consist of Verbal (V), Somatic (S), and Material (M) requirements in order to be casted. If a spell is labeled with V for Verbal, that means the character must make a verbal incantation in order to cast. Characters affected by spells like Silence will not be able to cast spells with this requirement. Somatic (S) means that the character must make a hand gesture in order to complete the spell, and Material (M) means that the spell requires specific components in order to cast them. Most spell components are simple to attain (such as a piece or metal or a rope), but some more complex spells can require expensive components, such as diamonds or rubies.
Spells cost spell slots to use. Spell slots can be compared to stamina or mana in the sense that they are resources used to cast a spell. Characters will have certain levels of spell slots available to them as they gain experience and level up. Like Hit Points, spell slots can be restored by taking a long rest -- or a short rest, if you're a Warlock!
(Wizard Spell Slot Table: Roll20)
Spells have a base level at which they can be cast/learned, and some spells can also be casted at higher levels by expending a spell slot at that level. For example, a Cleric can cast Guiding Bot at its base level 1 for 4d6 Radiant damage. For each level beyond 1st, players will add 1d6 of damage for the spell Guiding Bolt.
For a full list of spells, we recommend browsing 5eTools.
During combat, players can do several things: move, take an action, take a bonus action, communicate, and make a reaction. Movement is not part of your action, but some actions are limited depending on how much you've moved during your turn.
Bonus actions are the same as actions, but can only be used if your character possesses the ability to do so. For example, rogues can disengage or sneak as a bonus action. Monks can use extra attacks as a bonus action. These abilities are labeled as bonus actions in the player's handbook, 5e tools, or wherever else you reference your class actions and abilities during character creation.
After a big fight, your characters will feel pretty tired. It's just as important for your characters to rest as it is for you! Characters can take Long Rests and Short Rests when they are out of combat and in a safe location. Short Rests are only an hour long rest in which a character expends a Hit Die in order to regain some health. Hit Die are determined by character level and will be restored upon taking a Long Rest. Spell slots, unfortunately, cannot be restored during a short rest unless dictated by the class, such as with the Warlock class.
Long Rests take 8 hours, are usually overnight, and completely restore health and spell slots. While Short Rests can be completed in any safe haven or secret spot, Long Rests require setting up camp for the night or paying for a room at the local inn. No, you can't take a long 8-hour rest in the middle of the dungeon -- even if you're an elf and you don't "really" need to sleep.
For more information on resting, see the Roll20 compendium.