Why Don't Danes Understand My Danish?
You say a correct sentence and get a blank look, or a switch to English. It's rarely your grammar. Danish listeners lean on a few features of pronunciation, and when those are off, even perfect Danish is hard to follow. The list is short.
1. A vowel that turns into another word
Danish has far more vowel sounds than letters, and one small slip changes the word.
nininenynew
2. No stød, or stød in the wrong place
A catch in the voice that spelling doesn't show, and sometimes the only difference between two words.
hunshehunddog
3. Every letter, every word in full
The d in hund is silent, jeg is "ja", and hej, jeg hedder runs together as "hej-ja-hedder". Saying it all in full sounds like reading aloud, and if you don't know the short forms, you won't hear them either.
→ How Danes really speak: reduction
Where to start
Listening first. If you can't hear hun and hund apart, you can't reliably say them apart. The Danish pronunciation overview shows all of this in five everyday sentences.
If Danes switch to English as soon as they hear an accent, see how to practise Danish when Danes switch to English.