Important phrases. Here is a few:

Thank you = Tak (The A should be pronounced as the A in car, so it sounds like "tahk")

You´re welcome (after someone has thanked you) = Selv tak (pronounced "sel tahk")

Hello = Hej (pronounced like 'hi' in English)

Goodbye = Farvel (pronounced "fa vell")

Goodbye (informal) = hej hej 

Sorry = Undskyld (pronounced "unskyl")

Can you help me? = Kan du hjælpe mig? (pronounced "kan du yel-peh my"

I would like.... = Jeg vil gerne have.....  (pronounced "yi vil gehr-neh ha" ) (long i in yi, hard g in gehr")

Check, please = Må jeg bede om regningen? (pronounced "moh yi bay om ri-ning-en")

Film (for the camera) = Film

Ice cream = Is  (pronounced  "eees"

Cigarettes = Cigaretter

Soda = Sodavand

Water = vand 

Wine = vin (red = rød, white = hvid) 

Beer = Øl

Ticket = Billet

One = En

Two = To

Three = Tre

Four = Fire  (pronounced "fee eh")

Five = Fem

Six = Seks 

Seven = Syv (pronounced similar to the girl's name "Sue", the v is not pronounced)

Eight = Otte (pronounced "ohd deh")

Nine = Ni  (pronounced "nee")

Ten = Ti  (pronounced "tee")