First off you have to find all the suspects and interview them. Most of them will require bribing with money.
You can find the people you need to interview by following the markers on your navigation compass.
After successfully interviewing all the suspects you need to find the clues before you can accuse the guilty person. This is the tricky part and had me stuck for ages.
1. Go to Chanel's room (the mage) and look in the boxs on the table and find painting supplies. Don't take them cause that would be stealing
2. Go to the West Tower and down the ladder and look behind the boxes. Once you've found the painting, click on it and head back to the Main Hall.
3. Find the dining room and on the rug you should be able to find a smear of paint - not easy to spot. Click on it and then go and accuse Chanel.
She claimed she was painting the stars the night the painting disappeared but the others said it was raining bad. She was lying 8)