Most diacritical marks encountered in English come from borrowed words. French and Spanish words, for example, use diacritical marks to denote pronunciation and stress. Sometimes, these words will retain their marks in English to avoid confusion with native words. The most common example is the pair of acute accents that distinguish "résumé" --- meaning job history, from French --- from "resume" --- meaning start again. Tildes, as in the Spanish word for year, "año"; grave accents, as in the French word "voilà"; umlauts, as in the German wine "Gewürtztraminer"; and cedillas, as in the French word "façade" all make regular appearances.
Also known as "diæresis," this mark looks the same as the German umlaut and is usually used when two vowels are paired together but pronounced differently, as in the word "cooperation." Currently, the dieresis has fallen out of favor in English --- for example, you likely didn't miss it when looking at the word "cooperation" --- but it's still used by some publishers, most notably the magazine "The New Yorker," to ensure correct pronunciation and recognition --- "coöperation." In some cases, the dieresis has been replaced by a hyphen --- "co-operation," or "co-op."
Grave accents were borrowed from the French by English poets to lend extra emphasis to the final syllable, usually of a past tense verb. For instance, if a poet wished the word "cursed" to be pronounced as two syllables instead of the usual colloquial "curst," they would print it as "cursèd" to achieve "curse Ed." The word "grave" is pronounced not like the place you bury a body, but with an "ah" sound, and it derives from the Latin word for "heavy."
Acute accents look just similar to grave ones, but point up instead of down when reading from left to right. In addition to appearing as parts of borrowed words to indicate a bright pronunciation, these marks are used by scholars to indicate stress in lines of poetry. When a syllable in any given word is the most stressed, the scholar will place an acute accent over that syllable's vowel to aid in determining the meter, or rhythm, of the poem.
In dictionaries and other pronunciation guides, breves and macrons indicate the difference between long and short vowels. For instance, a long "o" sounds like "oh" as in "go" and is written with a breve --- similar to a half-circle --- above it; a short "o" sounds like "ah" as in "dot" and is written with a macron --- a straight horizontal line --- above it.