Let's look at 40 and 80: For some reason I get them confused, so I've made 40 green (it sounds like fir, which is green) and 80 red (it sounds like fierce, which I associate with red). That's easy enough.
Now let's look at 60 (and 80): Tres (60) comes from tresindtyve (tre-sinde-tyve), which means 3 times 20 Sinde is an old word (now obsolete) meaning times The same goes for 80: fir(e)sindetyve (4 times 20) = shortened to firs.
Now for the hard part: 50, 70, 90
The word halv here means the number minus a half (so halv 3 = 2½, halv 4 = 3½, halv 5 = 4½, and so on)*
50 = halv 3 x 20 = halvtredje-sinde-tyve - shortened to halvtreds.
70 = halv 4 x 20 = halvfjerde-sinde-tyve - shortened to halvfjerds.
90 = halv 5 x 20 = halvfem-sinde-tyve - shortened to halvfems.
Now, obviously you have to find a way to associate each word with a number instantaneously, the way I've done with 40 and 80 above. Learn them immediately and thoroughly, or they'll give you problems for many years.
* Similar to when you say, for example, that the time is halv tre (in Danish "halv 3" = 2:30)
