Both Norwegian and German are Germanic languages. Thusly they share a lot of vocabulary and pronunciation. Both have a /ø/ and /y/ as well as /ç/ a few others. Also English was influenced by the Viking raids in Britian. So we have a good few cognates as well as false cognates. Now, we will observe some of the cognates, how to find them and tell them apart.
Let's start with everything save Verbs. Here are a few words which are similar, if not the same, in Norwegian and German.
With pronunciation, German likes to use sch, when sk is prefered in Norwegian. Norwegian uses h a lot at the beginnings of words though it isn't pronounced.

Norwegian, German, (English)
Hund, Hund, (dog or HOUND)
Herr, Herr, (Mister, Man, Gentleman)
Familie, Familie, (Family)
Fisk, Fisch, (fish)
Luft, Luft, (air)
Best, beste, (best)
Medizin, Medizin, (medicine)
Direktør, Direktor, (director)
Morgen, Morgen (morning)
Dag, Tag (day)

Now, yes, a good few of these are modern words, but many are not. Now here are some Verbs using a similar format.
Reise, Reisen, (to travel)
Koste, Kosten, (to cost)
Vaske, waschen, (to wash)
Høre, Hören, (to hear)

So we can see some of those connections. Now let's see some other traits in Norwegian which are interesting to us English speakers. An interesting way to see some cognates to English (and to some extent German) is to take some of the ending letters off the english word.
Norwegian, English, German
Ha, Have, Haben,
Ta, Take, Nehmen,
Ni, Nine, Neun,
Litt, Little, Klein
Se, See, Sehen,
Komme, Come, Kommen,
Gi, Give, Geben,

Now, as for telling the languages apart. It's quite simple. Norwegian has only three extra letters, ø,å, and æ, whereas German has ö, ü, ä, and ß. Other ways to tell, is the use of Der, Die, and Das meaning "the." The noun ending -en in Norwegian is the same as adding "the." Also the pronouns are different save Du. Here are the different pronouns.
Norwegian, German, English,
Jeg, ich, I
Du, du, you (informal)
Han, er, he,
Hun, sie, she,
Det/den, es, it,
Vi, wir, we,
Dere, Ihr/Sie, You (informal/formal)
De, sie, they

Here are some other issues. Verbs when in a conjugated or finite form usually add -r to the end, where as German has a full conjugated form. Most infinitives in Norwegian end with -e as opposed to -en in German.

Not that German and Norwegian are easily confused (unlike Swedish and Norwegian, or worse yet, Danish and Norwegian) but here is an exercise that might help. Can you tell which is Norwegian and which is German?
åpne (verb) to open
Der Hund (noun) The Dog
Reist (verb) Travels
Hjelpe (verb) to help
Schule (noun) School
Kjøpe (verb) to buy
Ha (verb) to have
Hände (noun) hands
Bilen (noun) the car

I hope you enoy this, write me if you have any questions or linguistic comments.