Instructions
Load the Creature Creator via your in-game interface.
Open the "Details" sub-menu and select the wings you want to use. If you prefer the bug wings, called "Antisoptera," then you may initially have enough carry-over DNA points to buy them immediately. Bird wings, called "Cassoworry," cost 250 DNA and will likely require you to accumulate points before purchasing them.
Exit the Creature Creator and bite, damage, dance or sing with other creatures on your planet to gain DNA points. Singing and dancing correspond to buttons on your interface, but biting simply requires that you collide with a creature with your mouth facing them. Horns, toxic gas and other weapons help to lower their vitality faster.
Return to the Creature Creator, select the wings that you want, and attach them on your creature. As you move the wings along the creature's spine, legs, arms, head and other parts of the anatomy, it will automatically attempt to link the the wings to the body at several points, but it is up to you to click when they are where you would like them located.