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All you need to do these are your polishes, a paper plate or similar to put out some polish on, and a small dotting tool (or a toothpick, bent bobby pin, dried up ballpoint pen, etc.--though you could of course do these with acrylic paints and brushes if you prefer). After base coating I painted my nails with Jessica Surfer Boyz'n Berry (BTW, Jessica's website and the bottle disagree on where that apostrophe is supposed to go. I followed the website when I posted my swatches of this polish, but it's "Boyz'n" on the bottle. Totally fascinating stuff, right?! Yeah, anyway...). Other good choices might be China Glaze For Audrey, Essie Mint Candy Apple, Zoya Bevin or Wednesday, or a light, minty green like Sally Hansen Mint Sorbet or China Glaze Re-fresh Mint.
So once your base colour is dry, on every other fingernail, paint 3-5 irregular spots of bright pink (I used OPI Pink Friday, from the Nicki Minaj collection). These can be done with your dotting tool or, if it's small and easy enough to control, the polish brush itself. They don't need to be--really shouldn't be--perfectly round or uniform, and they should have enough room between for the leaves that come later.
After those have had a couple of minutes to dry, it's time to start detailing. With a dark pink or bright red (I chose Jessica Dynamic, a dark, berry-red pink), use your dotting tool to glide or stipple on a semi-circular swoosh, like a comma or a parenthesis, around about 1/3 of the flower.
Next, do a smaller comma/parenthesis across from it, leaving 1/4 to 1/3 of the border "open."
Your third swoosh will be a small comma from the middle of the flower to the open edge.
Letting those dry for a bit, use your dotting tool again to make polka dots (I've also seen stripes) on the other fingers. I used OPI My Boyfriend Scales Walls for mine.
When you've finished your polka dots, your darker pink swooshes should be at least semi-dry. Now it's time to add leaves to the flowers (I used Essie Pretty Edgy). These are also done with the dotting tool, dabbing/dragging three dots together into a triangle shape. Without really lifting your tool away from the nail, drag one dot into two at the base, near the flower, then drag the polish out to the point of the leaf.
After that, you're pretty much finished! Just give your polish ample time to set and dry before top coating. When it's ready, make sure you have a good amount of quick-drying top coat on the brush, and try to glide your brush over the top coat instead of making contact with the nail polish underneath. Also, avoid going over the same spot more than once if you can. These steps should help you avoid streaking your nail art, but even if you do get a little bit, it's a lot like the flowers themselves--from just a couple of feet away the tiny imperfections you might see close-up just sort of fade into the background, leaving you with cute, vintage-looking roses on your nails!