Relevant to note diacritic usage is language-specific, and sometimes different orthographies for the same language prescribe different things. And since the text did a great job explaining it for French, might as well exemplify with another language, Portuguese:

• acute ⟨á é í ó ú⟩ - stressed vowel in an unexpected position; ⟨á é ó⟩ are [ä ɛ ɔ]
• grave ⟨â ê ô⟩ - stressed vowel in an unexpected position; ⟨â ê ô⟩ are [ɜ e o]
• tilde ⟨ã õ⟩ - nasal vowel in a position where spelling ⟨n m⟩ would be awkward; typically [ɜ̃ ɔ̃~õ]
• diaeresis ⟨ü⟩ - omitted from newer orthographic standards, formerly used to distinguish ⟨qu gu⟩ /k g/ and ⟨qü gü⟩ /kʷ gʷ/ before ⟨e i⟩
• grave: ⟨à⟩ - grammatical aid indicating crasis; for most people it doesn't change pronunciation, although a few ones pronounce ⟨à⟩ as [ä:] in slow and monitored speech.