"Do you have a present for me?"
Translation:Har du en gave til mig?
Jeg køber en gave til hende. = I am buying a present for her.
Jeg køber en gave for hende. = I am buying a present on her behalf.
I'm not sure how to explain the exact differences in meaning between the two. If you speak Spanish, they're more or less like para and por.
Okay, this sentence implies that whoever has got the present is about to present it To her. I think "til" is used when the thing is going towards her/whoever.
If you know the dative case, it helps. English doesn't really use this but it's pretty much the difference between saying "She has a gift for the dog." and "She gave a bone To the dog."
In the first example, the bone is for the dog. In the second, she's moving the bone towards the dog. I hope that helps someone as a way of picturing the case here.