Have you viewed our tutorial, How to design a logo with Illustrator? It walks you through key tools and drawing techniques in Illustrator. After viewing it, you might watch some tutorials that are specifically chosen for a beginner to Illustrator. Go to the Illustrator section and click Show all tutorials. Then click Get started and view the 8-9 tutorials under Essentials for beginners.
Additionally, our training partner, Lynda.com features a course titled, Logo Design Techniques by Nigel French. Hope this helps!
Adobe Learn team