Hi,
A characteristic should be "colour" and you should have several values (black, white, etc).
Then, add that characteristic to the product and you should see the characteristics dropdown automatically on the product page.
If you still have troubles with the display of variants of a product on the front end, you should:
1. Delete all the variants of the product on the listing of variants that you can access via the button "manage variants" on the product edition screen.
2. Delete the characteristics of the product.
3. Save the product.
4. Add the characteristics again.
5. The system will regenerate all the variants automatically and you should be able to see the dropdowns properly on the front end.