Before taking my class, many of my students use a variety of Apps and are drawing with their fingers on their phones and creating amazing things!
Adobe has some great apps you can start with and I believe they are all free. Also, you may want to look at Sketchbook, both mobile and desktop from Autodesk.
For Android or Apple mobile devices:
Vector drawing anywhere.
Create production-ready assets anytime, anywhere.
Adobe Illustrator -- Buy Adobe Illustrator CC | Vector Graphic Design Software
Inkscape is an open source vector graphics app -- https://inkscape.org/en/
There are 7-day free trials for Adobe software, so you can try it out to see what works for you. If you're doing vector graphics for print or web design, try Illustrator CC:
If you're wanting to make vector graphics to animate, try Animate CC:
Try practicing by recreating logos you admire. Use multiple vextore shape layers so you can have multi coloured designs, and select all the layers and make into Smart Objects so you can store them to a CC Library.
I haven't used any software before.
this lets you get your toes wet without dumping code onto you and I've had good results from otherwise clueless (computers are scary) art people