The Pioneer Woman ran a cookie decorating tutorial last week that makes decorating seem easy and non-intimidating
http://thepioneerwoman.com/cooking/2010/12/decorated-christmas-cookies/

I was new to cookie decorating about a year ago.
Here are the crucial things you need:
pastry bag - I use these great disposable ones that come in a 10 pack (I think I bought them in Michaels) - because cleaning them is a pain, but any pastry bag will do

tips and couplers - a #3 or #4 piping tip should serve most of your needs - if you want to do any writing, you'll probably want a #1 or #2 as well. The couplers allow you to use the same bag for different tips without having to empty it.

toothpicks: these are great for two things - a) to put the food coloring into the frosting (I always use gel, not liquid) and b) once you pipe on your frosting, a toothpick is perfect to gently nudge it to cover all the spaces.

I also keep on hand: paper towels, a small bowl of water for dampening towels (to clean off crusted up tips) and I like to use a tall glass or pitcher to fill the pastry bags with.

Whew, hope that helped! You can see some of my experiences on my blog: http://www.bakingandmistaking.com/search/label/cookie%20decorating

You can create some great designs using edible sugar paper. Create layers of 2 or 3 different colours in a decoupage manner and stick them with some very thin icing or sugared water.

I too loved the Pioneer Woman's post last week.

Have to to say it, a ziplock bag is all you need as far as pastry bags go (having to tops be sealable is a real plus). And a large bowl if you want to go with something where you do the background all one color, dipping is way more efficient than piping you can put another design on top or swirl it in while it is still moist.

These are the short cuts I have learned over the years. My mother, sister, and I bake rooms full of cookies every year. And from this I have learned no matter how beautiful a cookie is it doesn't matter unless the cookie and frosting are bomb, so focus on that.

I'll second and third what others are saying about the Pioneer Woman's post with the additional comment that her post was based on time she spent with the author of Bake at 350. http://bakeat350.blogspot.com/ I used her royal icing recipe this past weekend and LOVED it. She also is a wealth of information regarding designs and cookie recipes.

If you're going to be doing any flooding (which is how they achieve that nice smooth glossy look, you should also pick up a couple of flooding bottles at Michael's.

Looks like everyone covered the basics already! And Bridget from BAke at 350 is one of my fave blogging friends and cookie decorators. Can't go wrong there. Check out her University of Cookie site for video tutorials.

My tools:
--12-inch disposable decorating bags (wilton brand, from michaels/craft store)
--standard couplers (wilton, from michaels)
--decorating tips (size 4 and 5 outline, size 2 and 3 for details/writing)
--rubber bands (use to close filled frosting bags)
--MERINGUE POWDER (also at michaels, you'll use this to make your icing, not usually found in the supermarket, so don't forget it on your craft store run)
--food coloring. (you'll find concentrated pastes in tubs at the craft store. Lots of colors, work well, but a bitter taste. I use Americolor soft gel pastes exclusively. Find 'em online or at specialty cake decorating stores)
--toothpicks (already noted, great for unclogging but also spreading icing when flooding)
--scissors (to snip ends of bags)
--sprinkles (fine sprinkles or sanding sugar, great easy decorating tool)
--underbed storage boxes (great if you have cats. I stick a whole tray of cookies in these to allow cookies to dry overnight safely)

Well, the tool to make the cookies in the photo would be a toothpick . . .

Ice the cookie with one color, add a spiral or straight lines with the second color, and use a toothpick to marble.

I LITERALLY just got done decorating my cookies using PW & Bake & 350's tutorials!! I did Xmas trees, wherein I marbled green & white for a 'snowy' effect; and stars swirled to look like peppermint candies. SO easy and SO cute!

I've always liked a site called Karen's Cookies. I found it a few years ago when I was just beginning to bake. It provides lot's of recipes, how-tos, videos, etc.
The site also had printable practice icing sheet which has been super helpful for me.