You probably want to read the user manual for the ST libraries, the source code / header files, and compare them vs. the device datasheet. CoIDE offers a lot of examples and that helps greatly.
Learning the vendor library is no small task and if you don't have a middle layer, it is frustrating as well.
The usual sequence is this:
1) write a series of house-keeping stuff: how do you want to initialize the mcu, which ports to turn on / off, how to name the leds on the board, how fast the device is running, software delays, etc.
2) write a series of functions / macros to operate the gpio: set/clear/flip pins, put them in input/output mode, PP vs. OC, how fast you want them to run, etc. At this point, you should be able to blink the leds;
3) write a few routines to run systick: typically to set its irq frequency, and being able to install a user handle for the systick isr; At this point, you can blink the leds with the systick, and then you can go back to 1) and recalibrate the software delays;
4) write a series of timer routines: you should be able to specify how often a timer triggers and being able to install the timer isr; You can then blink the leds with timer isr. They are a ton of them on the STM32F3 board;
5) write a series of pwm routines: you want to utilize the OC/pwm features of the timers and do hardware pwm. You will then deal with the AF functions of the chip -> confusing; The above will allow you to control a motor;
6) ancillary routines, like spi, i2c, uart (at least tx), adc, and rtc, etc.
7) if interested, you will also write a few routines to read the onboard mems sensors.
It will be a good learning and challenging experience, especially if you haven't dealt with the device before.