There are many interesting processes that work on languages which contribute to their change over time. Prepositions (or postpositions, in other languages) quite commonly become glued to the beginnings or ends of words (or even the beginnings or ends of roots in words). They go from being prepositions to being pre- and postfixes, and in many cases quite regular, thus prepare and prescribe (or indeed, prefix) have the same suffix pre in the sense of before/prior to. In some cases, they continue to exist both as prepositions and prefixes, in others they survive only as prefixes.
I will focus mostly on prepositions here, because they are quite instructive in mapping words from Norwegian to Dutch. They basically correspond to syllables, even if not all syllables here listed are prepositions.
It has to be said also that just because the same word exists in two languages (as described by these translations), it might not mean the same thing. I've tried as much as possible to use words that correspond both in composition and meaning.
Now, I'm quite sure that encyclopedias have been compiled of this information, but I find it more fun to notice things myself than reading the encyclopedia. The cases you will see here are by no means an exhaustive list, merely the ones I have noticed (and can recall). You will discover your own patterns (and that, in my view, is quite satisfying).
Syllable translations
av -> af/van
avfall -> afval {garbage}
avhenge av -> afhangen van {to depend on}
av -> uit
avsette -> uitzetten {to expel}
kle av -> uitkleden {to undress}
bi -> bij
bidrag -> bijdrage {contribution}
bistå -> bijstaan {to assist}
for -> ver
forgå -> vergaan {to perish}
forlate -> verlaten {to abandon}
for -> voor
forbi -> voorbij {elapsed}
forberede -> voorbereiden {to prepare}
forekomme -> voorkomen {to occur}
het -> heid
mulighet -> mogelijkheid {possibility}
nødvendighet -> noodzakelijkheid {necessity}
-ig -> -ijk
mulig -> mogelijk {possible}
nødvendig -> noodzakelijk {necessary}
opp -> op
oppstå -> opstaan {to rise}
på -> op
påfallende -> opvallend {remarkable}
vente på -> wachten op {to wait for}
til -> toe
tillate -> toelaten {to allow}
tilstand -> toestand {condition}
u -> on
umulig -> onmogelijk {impossible}
utrolig -> ongelooflijk {incredible}
ut -> uit
utebli -> uitblijven {to fail to appear}
uttrykk -> uitdrukking {expression}
Consonant changes
I think most of these are pretty obvious, because the sound you hear is very similar, so it's more a spelling change than a sound change.
f -> v
falle -> vallen {to fall}
fare -> gevaar {danger}
k -> ch
makt -> macht {power}
vitenskap -> wetenschap {science}
kj -> k
kjenne -> kennen {to know}
kjøkken -> keuken {kitchen}
s -> z
svømme -> zwemmen {to swim}
synge -> zingen {to sing}
sønn -> zoon {son}
hv/v -> w
hvilken -> welk {which}
hva -> wat {what}
gevinst -> gewin {winning}
vinner -> winnaar {winner}
Vowel changes
The vowels are more substantial. Going from lyd to geluid is y to au in Norwegian phonology, which is pretty big. Dutch is packed to the brim with diphthongs (a single vowel that actually goes from one sound to another, like "au" or "ei", typically spelled with two letters), so there is a huge amount of these that you have to learn to match with their spellings.
e -> ei
egenskap -> eigenschap {property/attribute}
kreativitet -> creativiteit {creativity}
i -> ij
bli -> blijven {to remain}
fri -> vrij {free}
tid -> tijd {time}
o -> oe
million -> miljoen {million}
u -> ui
bruk -> gebruik {use}
y -> u
fylle -> vullen {to fill}
fyre av -> afvuren {to fire off}
y -> ui
lyd -> geluid {sound}
tydelig -> duidelijk {clear}
æ -> ee
ærbødig -> eerbiedig {reverential}
ære -> eer {honor}
ærlig -> eerlijk {honest}
ø -> eu
seriøs -> serieus {serious}
ø -> oe
prøve -> proef {test}
søke -> zoeken {to search}
øve -> oefenen {to rehearse}
å -> aa
gå -> gaan {to go}
måltid -> maaltijd {meal}
slå -> slaan {to hit}
Decoding
So how does it work in practice? If you're learning Dutch it won't take very long before you see the common word onwaarschijnlijk. At first sight it's a pretty scary word with crazy vowel combinations. But if you take the above list and work in the opposite direction you discover than you can split off on which is a negation. You now have something that begins with waar and since that is also a common word you probably already know that it means sann {true}. You also know that lijk is a common suffix that corresponds to lig (which is used in adjectives), so with the parts you have you can make usann-lig, which in all probability completes to usannsynlig {improbable, more literally: not-true-looks-like}. You check the context and confirm that it has to be an adjective, and that this meaning fits well.
As a matter of fact, this is exactly how I understood the word the first time I saw it. This is actually quite a good example, because it shows how you can do this with partial knowledge. There are two parts with perfect correspondence, on/u and lig/lijk. But waar is a different root from sann, and this I had to know about. I did not use schijn at all, because it didn't look like anything I knew. But I now know that it would have been a blind alley, because synlig {visible} does not correspond to schijnlijk (which is not even a word). schijnen means to seem, which I didn't know at the time.
A similar example is ongelooflijk = utrolig, where you need to know that geloof = tro {belief}, thus "unbelievable".
Now, you might think that trying to painstakingly work this out on paper sounds about as appealing as cleaning a warehouse with a toothbrush. But, of course, the point is that your brain does this to a great extent unconsciously. Sometimes you think you understand a word and you can't even figure out why, it must somehow have found an association that you're not conscious of.