I assume you’re writing in American English, but you might still encounter accented characters in foreign words. Foreign words arise in two situations:
In proper names, like people and places (Albrecht Dürer, François Truffaut, Plácido Domingo). In names, accented characters must always appear accurately. Otherwise, the name is misspelled.
In loanwords used in American English. Some of these words have become citizens and should be spelled without accents (naive for naïve, melee for mêlée, coupe for coupé). Others have not and should not (cause célèbre, piña colada, Götterdämmerung). Check a dictionary or usage guide.
How do you type these? Consult the chart of common accented characters.
Proper names are not italicized, but loanwords sometimes are, depending on their degree of assimilation. Again, check a dictionary or usage guide.
The German letter
Eszett(at left) is technically a ligature, not an accented character: it takes the place of ssin a word like Straße. Unlike ligatures in English, its use in German is not discretionary—Germany has adopted rules for when it must appear and when it must not. (To the surprise of no one.) Switzerland, meanwhile, disregards the Eszett, and just uses ss. And no one uses the Eszett with all caps. I mean, except those who do. So it’s best to follow Switzerland’s lead and ignore it. Even if you place the Eszett correctly, it’s less common to readers of American English than the usual accented characters, and it can easily be mistaken for a letter B or a Greek beta ( β).