How do I go about “part-by part practice”?

Have a clear goal. Don’t just repeat it recklessly.

Once you’ve decided the bowing and fingering patterns for the bracketed part to a certain degree (although you may change them later on), you need to practice the part until you are completely confident in yourself. If you feel that the bracketed part is no longer a problem for you, add a few bars preceding and following the part and make that into one phrase. Play the whole phrase through and see if you can still play the bracketed part without an error. It is a very common phenomenon to make the same errors in the exact same part again as soon as you add a few more bars.
If this happened to you, take a moment and ask yourself why. Is it your bowing pattern? Or is it your fingering? More often than not, you may be able to solve the problem you make with a small change. Here’s an important tip. When you make an error during practice, don’t panic. You need to think why it happened. It has an adverse effect if you keep practicing without thinking about the reasons for the errors: like you are practicing to make the same mistakes again and again.
If you don’t take the time to figure out the reasons, which takes only a very little bit of time, you may not be able to fix the problem even if you practice for tens of hours. So, get in a habit of putting the instrument down when you make a mistake, and think why you made the mistakes!

If you cannot figure out a reason for making errors, talk to your teacher and work together to find a solution. Once you found the reason and fixed the problem, play through the phrase that includes the bracketed part one more time. If you could play it without an error, play it more than 5 times and see if you can play it naturally without any errors. If you find no problems, go on to the next bracketed part and repeat the same procedure. After you finished all of the part-by-part practice, play the entire piece in a slower tempo again. If you find different sections that need to be bracketed, mark them and practice the same way. Have this practice repeatedly while you still have the time before your performance.

When you are trying to master a piece of music, make sure to follow this pattern: Play the entire piece through – part-by-part practice (practice bracketed parts) – Play the entire piece through again. Also, it is important to start your practice with a different bracketed part each time.