Was Finland occupied during World War 2?

No: fighting the Soviet Union twice during WW II, Finland lost about 93,000 soldiers but retained her independence.
Yes, when Hitler and Stalin came to an agreement in 1939 on how to divide Eastern Europe, it was agreed that the Soviet Union would enter negotiations with Finland for concessions. Finland refused to work with Russia which resulted in the Winter War and the Soviet annexation of part of Finland. Soon after, Finland decided to work with Hitler in his attack on the Soviet Union, and from the onset of Operation Barbarossa in 1941 they allowed Nazi troops to occupy Finland.