The easy nail designs to start fall into the following general categories:
Two-tone nail polish treatments, basically making your nails half colored and half colored. It is fairly easy to do and can create some very abstract patterns, but be careful in terms of having a steady hand to get the lines right.
Adding a smashed effect to your nails with Crackle Nail Polish. Easy, and create totally unique designs, especially with the almost infinite variety of color combinations between the solid base coat and the top crunch polish.
By making your fingers one color, and your thumb a different color [an alternative is to make your little finger a different color, or your thumbnail]. This is tricky, because if the colors don't complement each other well, it just looks like you started a nail polish job and got bored halfway there!
Draw designs like flowers, ladybugs, stars, etc. This is really easy to do and involves using a toothpick as a brush and nails as a canvas. The problem is that if you're not careful, the flower design you just completed may seem too similar to others you see in the city.
Magnetic Nails - This is the latest high-tech trend, and it's pretty easy and creates very unique designs with special magnetic nail polish and what looks like stamps, but are magnets that place metal particles on the nail around a design.
Nail Pens: They're fun and they're like drawing on your nails with markers [except they have nail polish!]. I personally like to make abstract patterns and swirls on my nails with these as it doesn't require the same level of precision as trying to draw.
Nail Stickers - Special "small" stickers that adhere to a properly applied nail or nail polish and will not smear or distort when coated with a clear nail polish. It's a bit messy if they get scratched or torn and then have to be removed, but this can be a quick design that doesn't take long.
Gel or Gel Nails: These are not strictly nail designs, but when used properly gel nails can last up to 3 weeks without chipping or cracking, they dry very quickly under UV light and making designs with them will result in a more durable design. The speed is also often faster since UV light is used to dry the enamel in less than 2 minutes.