Hello! I started out with ncoll36's
Minimalist Wallpaper Guide | Inkscape. Take a look at it and practice with it until you get a hang of the basics. All you really need is Inkscape, a free vector software. Be sure to read the description, he links a few other things as well.
Once you've got the basics of Inkscape down, then its just practice and finding your own style I guess. You can find reference images through Google or just by taking screenshots of the anime itself.
Let me know if you do start making stuff! I'll be your first watch lol.