Cover, Crits, and the Art of Not Dying
Cover is one of those rules that sounds obvious until someone at your table starts arguing about whether advantage cancels it out. It does not. Half cover is a flat +2 to AC and Dexterity saving throws. Three-quarters cover bumps that to +5. Total cover means you simply cannot be targeted, full stop.
The saving throw interaction with cover is worth getting right. When an area of effect spell catches you, your cover bonus is calculated from the perspective of the spell’s point of origin, not from where the attacker is standing. If a fireball goes off behind your rock and you have half cover from that direction, you get the half cover bonus to your Dex save. The spell is the archer now.
Crits and Damage
A natural 20 doubles your damage dice. Not your modifiers, just the dice. Roll the d8 twice, then add your Strength or Dexterity modifier once. This is one of the most house-ruled corners of 5e, and honestly the raw version has a real problem: you can roll two 1s on a crit and deal less damage than a normal hit. Whether you fix that by guaranteeing a max die, doubling the total roll, or just adding extra dice is between you and your table. The rules give you a floor, not a ceiling.
Damage Types
Bludgeoning, piercing, and slashing are your bread and butter physical damage types. The elemental ones are mostly self-explanatory, with two exceptions worth flagging. Force is essentially the catch-all for pure magical energy, think Magic Missile, things that are clearly a spell but don’t fit anywhere else. Thunder is concussive, percussive damage, closer to a shockwave than an element. A grenade, if your setting has one, is probably thunder. The two get confused because they both feel like “generic magic impact,” but the distinction matters when resistances are involved.
Poison is also worth mentioning, specifically to say: most things are immune to it. Build around it at your own risk.
Going Down and Getting Up
Dropping to 0 hit points starts the death saving throw clock. Roll a d20 at the start of your turn: 10 or higher is a success, and you need three of either before the other to live or die. A 1 counts as two failures. A 20 brings you back to 1 HP immediately.
Instant death is a separate and nastier rule. If a single hit reduces you past 0 by an amount equal to your maximum hit points, you die outright, no saves. At low levels with single-digit hit point pools, a bad fall or a crit from something that should not have been in that encounter can trigger this. DMs tend to quietly not apply it, and that is probably the right call more often than not.
Temporary hit points sit outside your normal pool entirely. They absorb damage first, cannot be healed back through spells or potions, and do not stack. If you get a new source of temporary hit points, you choose which to keep, not both. They are a buffer, not a bonus pool.
For further reference, the relevant sections are in the Player’s Handbook Chapter 9 (Combat), specifically the Cover, Damage and Healing, and Hit Points subsections.