- Ich mag keine Orangen, aber ich mag Äpfel.
- Ich mag Orangen nicht, aber ich mag Äpfel.
In fact, both sentences are correct translations of the English sentence "I do not like oranges, but I like apples." It depends on the context and one's personal preference which sentence is used.
The first sentence is unmarked in that it simply enumerates two information: (1) you don't like something; (2) you like something else. The connector aber indicates that both information are in contrast. Consider the following example dialogue:
A: „Was soll in den Obstsalat?“
B: „Hm, also ich mag keine Orangen, aber ich mag Äpfel. Und Kirschen ...“
The second sentence emphasizes this contrast a bit more, and it is typically used when the thing you don't like was already mentioned before:
A: „Wollen Sie vielleicht ein Netz Orangen?“
B: „Tut mir leid, ich mag Orangen nicht, aber ich mag Äpfel.“
A: „O, da kann ich diese hier empfehlen ...“
Or when you were explicitly asked what you do not with an emphasis on the word nicht:
A: „Was mögen Sie nicht?“
B: „Ich mag Orangen nicht, aber ich mag Äpfel.“
Anyhow, using the first sentence in the last two dialogues would be correct, too.