Vector graphics software
There are a few options out there to draw vectors.
Vectr is a software you can use online, great for beginners. Have a look at this introductory video:
Inkscape is another one that you will be able to download to your desktop for free. It is similar to Adobe Illustrator and allows you to draw vectors and export them to use on the laser cutter.
This below, is the first of a collection of videos on youtube that introduce you to the use of Inkscape.