More figuring things out for myself and posting it here so I can refer to it later.
- A spell that requires a somatic component can only be cast if you have a free hand (PHB 203).
- You can cast a spell with a somatic component while wielding a two-handed weapon because a two-handed weapon only requires one hand to hold it, leaving you with one free hand. (Weapons with the Two-Handed property only require two hands when you attack with them, PHB 147.)
- If you are wielding items in both hands (such as two-weapon fighting or wielding a sword and shield) you can stow one item for free and then cast a spell with a somatic component because you now have one free hand (PHB 190). On your next turn you could draw the weapon for free and attack with it.
- You can't stow an item as part of a reaction, so spells that are cast as reaction and require somatic components can only be cast if you have a free hand. (Shield is a particularly troublesome spell in that regard.)
- The War Caster feat allows you to cast spells requiring somatic components when you are holding weapons or a shield (PHB 170).
Somatic and Material Components
- If a spell requires both a somatic and material component, your free hand can be used for both (SA).
- Clerics and paladins can inscribe their holy symbols (their spell foci) onto a shield and use the shield hand for both somatic and material components (PHB 151).
- However, if a spell requires only a somatic component (and no material component) and you are holding a spell focus in one hand and another object in the other, you need to stow one of them to be able to cast the spell (SA).
Spells Per Turn
- If you cast a spell as a bonus action, you can also cast a cantrip with a casting time of 1 action on your turn (PHB 202).
- If you have access to the fighter's Action Surge ability, you can cast multiple spells that require 1 action to cast. However, if you cast a spell as a bonus action, the spells you cast with your Action Surge actions must be cantrips (SA).