Sink Pipe Broken

Hard to tell from photo, looks like it came loose not broke.
Unscrew the nut from the sink, slide it over the pipe, and will be a plastic bushing or washer that slides over the pipe. As you tighten the nut back down, will put pressure on the bushing and hold it in place. Be sure to clean and wipe everything with a rag, only hand tighten and do not use a wrench.

As you can see, is not much to it, if you bump the pipe to many times or pile to much crap under the sink and put weight on it, it can come loose. Is possible whoever installed it cut it to short and is pulling out.

It is called a kitchen sink drain kit, is $7 at home depot. If you need to replace it.
Will need a hand saw of some sort to cut the pipe to proper length.

My thingy bobber is still broke and cant post photos again
http://www.homedepot.com/catalog/productImages/300/e9/e9b239bd-424c-44bf-8c43-b809798fb411_300.jpg

I should have waited for second photo to appear, shows much more.
Still looks like it came loose and may be able to just put it back together.
But what is all the crap around the joints?

To replace it all, is called a double basin kitchen sink drain kit, and you need to be sure you get a tail piece with the dishwasher drain also.
May be a kit with the piece included, or may need to buy it separate.