

Draw Shape
Create a new file in Adobe Illustrator and draw a circle on the page (we added a black stroke so you can see what's happening).

Type Tool
Hold down the left mouse button over the Type Tool until you see more options appear.
Choose the option : Type on a Path.

Text Anchor
Hover over the path with your mouse and ensure the Word Path or Anchor appear in pink where the cursor is, then click on the path.
Place Holder text fills the outside of the shape, as shown.

Type
Type using your keyboard.
Then use the Direct Selection tool (white arrow) to hover until the curser changes to a horizontal arrow and vertical line icon.
Click and drag to rotate text around the shape.

Options
Navigate to:
EffectPath > Type on a Path > Type on a Path Options...
This allows you to change the look of the text.
Flip
This will flip the text across the object.
Align to Path
This allows you to change your alignment on the path.
Spacing
This will alter the horizontal spacing between each letter.
Preview
Display results of selected options.

Flip Text
Duplicate the object and change the Spacing to 100.
Your result will look like the example shown.

Rotate
Now we just need to flip it :
180 degrees.Transform > Rotate...

Align
Select both shapes and align horizontally and vertically.
Select both shapes and align horizontally and vertically.

Complete
Add some bits & bobs, then our artwork is complete.
A finished copy of the artwork can be found Here