Use a base coat on the nail before you apply the colored nail polish, to protect your nails.
Apply a nail color - this will be your base color - starting from middle of your nail, using smooth uniform strokes, then allow nails to dry.

Take a colored nail polish and a toothpick - you can also use a multi-purpose nail sticks from the drugstore, even a needle, but make sure it's thick enough.

Apply 3 dots with the nail polish to the nail, get the toothpick and start dragging the color on the nail, creating unique nail art designs. Let them dry and apply a top coat to prevent colors from chipping and make your nail polish last longer.

You can also create flower nail designs by following these steps:

Take the nail polish that you want the middle of the flower to be and apply a drop on a piece of paper.
Take the toothpick and pick up some color with it and make a small dot wherever you want the flower to be ensuring you leave enough space for the petals.
Take the other color and drop a bit on the paper.
Using the other end of the toothpick take a bit of nail polish on the tip. Apply it next to the other dot.
Take again more nail polish on the toothpick and make another dot next to the last one leaving a tiny space between them. Do the same until you have circled the first dot.
You should now have a tiny flower on your nail. Leave the nail polish flowers to dry and apply a top coat with quick strokes so the flowers won't smudge.

Once you learn the basics, you can easily create your own nail art with intricate designs and lots of colors - use your imagination and have fun with it!