Danish for to like is at kunne lide.

Warning: As you can see lide goes together with kunne. If you omit kunne in the lovely sentence jeg kan lide meget (I like a lot (of things)), it becomes Jeg lider meget (I suffer a lot) as lide on its own means to suffer(!).

The Danes tend to pronounce it as kunne li' - keep it short, you don't sound out the 'de' - opposed to suffer where you sound out the whole of the word 'lide'.

Do you like..?
			Kan du lide kaffe?	Do you like coffee?
Yes
			Ja. Jeg kan godt lide kaffe	Yes. I like coffee
No
			Nej. Jeg kan ikke lide kaffe.	No. I don't like coffee
Correcting
			Kan du ikke lide te?	Don't you like tea?
			Jo, jeg kan godt lide te	Yes. I do like tea	You say 'jo' instead of 'ja' when you are correcting someone
You say 'jo' instead of 'ja' when you are correcting someone
I like both
		p	Jeg kan både lide te og kaffe	I like both tea and coffee
I don't like either
		p	Jeg kan hverken lide te eller kaffe	I don't like tea or coffee
Preference
			Jeg kan bedre lide te end kaffe	I like tea better than coffee

Notice that godt [lit: well] is added when say you like something.

Godt can be left out but Danes usually keep it in as to emphasize that yes they do like this or that.