You only need clear coat, one color, and a nail art pen for this.
Start with a base coat, and then coat your nails with the color of your choice.
The next thing you'll need is your nail art pen so you can draw on the zebra design.
I don't know about you, but I needed something to go by since I don't stare at zebras all day long. To remedy this, I just did a Google image search of zebra print and got all kinds of results. When I found something I liked, I sort of followed it to make it look right.
I pulled it up on my phone since it was right beside me...
Then just continue doing the design on every nail.
Keep in mind that zebra print is irregular. It's not simply stripes, and it's not a repetitive pattern. Just study a photo for a few minutes, and you'll soon see how it works. (You may think it looks funny when you've only finished on nail, but don't worry. The design looks much better when it's on all the nails.)
Let the black dry completely, and then finish with a clear coat.
Viola! You have zebra print nails!
Enjoy, and hope you have a great weekend!