Usage patterns
机の上に〈物〉を置くto put something on the desk
I put the book on the desk.
机の下に隠れるto hide under the desk (e.g. during an earthquake)
During the earthquake, I hid under the desk.
机を片付けるto tidy up one's desk
I tidied up my desk before starting to study.
Expressions
机に向かうsit at a desk; be at one's desk; set to work on revision, homework, etc. 机を並べるwork together; be classmates; sit side by side