Accents aren't extremely common in Dutch — definitely not nearly as common as they are in French — but they're certainly more common than in English. There are a few special diacritics (marks above letters) that you'll come across when studying Dutch:
Incidentally, these are all diacritics that can be found in French as well. I've linked Wikipedia articles on each type of diacritic so you can learn more about them, but here's a little summary of what you should know:
The acute accent can change the sound of the vowel — like in the sentence this discussion is for — or it can be used to place stress on a vowel in writing since you can't convey stress like when you're talking. Here's an example the Wikipedia article gives:
Dit is ónze auto, niet die van jullie. = This is our car, not yours.
The accent above the o in onze conveys that that word should be stressed.
Unfortunately I don't know too much about how the accent grave works in Dutch. The only thing I can really say is that it seems to often be used in words taken from French.
The dieresis is a rather interesting diacritic. I see that you've studied a bit of German on here, so it's likely you're thinking, Hey, that looks like the umlauts German uses! That's because they do in fact look identical, but they actually have rather different functions.
The umlaut changes the way a vowel sounds, whereas the dieresis is used to mark another syllable; in other words, it lets you know that two vowels aren't part of a vowel combination. We can look at an example of a word used in English that uses a dieresis: naïve. Normally when you see the vowels a and i together they combine to make a sound like the word eye, but the dieresis above the i indicates that the vowels should be separate, creating a different pronunciation. The same thing happens in the Dutch word for Ukrainian: Oekraïens. The dieresis above the i indicates that the vowels i and e should combine and not the a and i, making it sound like ooh-krah-EEns.
Sorry for turning a relatively simple answer into a long explanation, but hopefully you'll find this information useful and interesting. ^_^
Firstly, heel erg bedankt - thank you very much! Mighty well explained, although in my engineering studies I've come to mistrust Wiki completely. The coolest thing about Oekraïens is that Ukrainian language has a specific letter "ï", which is pronounced "yi" - like "one, 1" in Chinese only in a regular Western emotion-based tone. No other Slavic descendant's alphabet has such a letter in it, which makes me wonder, upon you mentioning Ukraine here, during a discussion on Dutch and French, whether those countries had a connection more distinct than Peter I learning Dutch culture and cultivating it in Russia. Mind you, this had been before Ekaterina II who split Russia in three: Red Russia or simply Russia, White Russia (Bela Rus'), and Small Russia (Mala Rus'). Small Russia was on the edge of Russian Empire, a tiny piece of land always suffering conquests from both Poland and Russia, and so was called Ukraïna, literally: "The country by the edge (u kraya)". With this said, how did ï really make it into Ukrainian alphabet?