Once inspiration strikes, you don't want to miss it. Millions of great ideas have been lost to the world because somebody forgot to write it down, or thought "I can remember that" and forgot it forever.
Having a notebook not only lets you draft and sketch ideas immediately once you get them, but having that tool at arm's reach also means that you'll be more aware and finding inspiration when/where you normally would've missed it. Having a log of all your ideas, good and bad, is also a great tool because then you can look back on them with fresh eyes at any time.
When it comes to starting any project, the more tools in your belt, the better. This doesn't necessarily pertain to physical tools, the mental ones are even more important. Start by reading up on some of your favorite fashion designers. What's their process? How do their designs speak about them as people? Also learn about how clothes are made to get a better understanding of what you'll be doing as a fashion designer.
Take time to also learn about design as a whole. Colour theory is a great place to start. Then, what looks good with what, or what looks bad with what. Once you have a basic grasp of these ideas, and a basic knowledge over fashion design, then you can branch out and expand your imagination into broader, more abstract thoughts. Then, you can start designing and finding your own personal style.