I'm wondering what are the basic ways that accent marks should be used when coming up with fantasy names of people, places, etc. Sorry if this might be a little vague of a question.
Accents are not decorations. Have a reason for using them beyond "I'm writing fantasy and they look cool." (The same goes for apostrophes.)
In addition to Daniel's very good answer:
- An accent may indicate not just spoken vs. silent but a completely different word. See the differences between des, dés, and dès here (of, dice, and since respectively) and côté, côte, and cote here (side, coast, and stock).
- An accent can change the pronunciation of a vowel. The umlaut (not a native English diacritical mark) over a vowel in English generally means that the vowel is written once but said twice: naïve is said nye-eve, not nave. This is why you might occasionally see cöoperation, to make sure you don't think it should be coop eration.
- Accents may be required by pronunciation, or change it. The cedilla makes a C soft (François is Fran-swah, not Fran-kwah). The tilde adds a vowel to an N (jalapeño is hala-pee-nyo, not hala-pee-no).
- Sometimes accents are used to indicate historical orthography. The circumflex over a vowel in French means that at some time in the past, the word had an S in it. Hôtel used to be hostel, maître was maistre, and so on.
- I don't speak or read Hebrew, but I know that it's written without vowels, and the accent marks (dots) indicate what the vowels are. More discussion here.
This question might also be useful: How can I effectively invent a language?
If you want a more thorough discussion of creating a language, known as a conlang or constructed language, I highly recommend David Peterson's The Art of Language Invention. Peterson created languages for Game of Thrones and Defiance, among other properties.
Understand what an accent mark is
There are many kinds of accent marks. For example, the acute accent in French signifies that the 'e' is to be pronounced at the end of a word. This is the most common use of the acute accent.
You want to use accents to clarify your meaning or pronunciation. They should be used to make difficult pronunciations clearer. If you know what the accent will be interpreted as and it is necessary, then feel free to use it!