Try working it out yourself on paper first. Decide on a few start and stop times and work out the fees for each block. After you've done a few you'll get the hang of how to do it and at that point you'll be able to start coding it up.
So for example let's say she works 1830-0100. That'll be 1.50 per hour from 1830-2100 (how many hours is that, then multiply the number of hours by the rate), 1.00 per hour from 2100-0000 (same: hours * rate) and 1.25/h from 0000-0100. Then work out the total price.
You'll need to get some input from the user - just four numbers, which for the above example would be 6 30 1 0. Check the numbers are in range and display an error if they're not. Then if the numbers are correct, proceed with the above calculation. The assignment doesn't say anything about checking validity of the minutes but you should add that anyway.
Also work it out step by step. Start with the input and the validation. Make sure that works before moving on to the next step. Then write the code for the first time zone (before 9pm) and display the time, rate and fee just for that block, and make sure this matches your calculations for that zone. Then add the second zone and test, and finally the 3rd zone (after midnight). While you're writing the code you can display a lot more than the final program will, just so you can be sure you're on track. Once the program is complete you can remove the extra output so that the program just outputs a single number - the fee for the overall event.
Take it step by step and it becomes really easy. Trying to write the whole lot in one go is probably where you're getting lost.