Typekit is now Adobe Fonts.

What you'll need
Create a new document and set up your workspace. Bring in a reference image to use as inspiration, and use the Layers panel to easily manage your artwork.
Combine rectangles, triangles, circles, and freeform shapes to build your artwork. Use Smart Guides to align the various elements.
Round out your logo by adding the business name using the powerful typesetting features in Illustrator. Creative Cloud members can choose from the vast library of high-quality typefaces from Adobe Typekit.
See how your logo looks on mockups of everyday items, like t-shirts and business cards. And learn how easy it is to save your logo artwork for printing, sharing as a PDF, posting on the web, and more.
Learn more about Creative Cloud for teams and business logo design.
Contributor: Brian Wood