General:
* Hit the books: This is a very common idiom for studying.
* Burn the midnight oil: This means to work or study late into the night.
* Dig in: This means to start working diligently on something.
* Put your nose to the grindstone: This means to work very hard and focus on a task.
More Specific:
* Get your head down: This means to focus on your work and ignore distractions.
* Cramming: This means to study intensively in a short period of time, usually before an exam.
* Brush up on: This means to review something you've learned in the past.
* Bone up on: This is similar to "brush up on," but implies learning something new or studying in more depth.
The best idiom to use depends on the context and the specific meaning you want to convey.