Your options seem to boil down to connecting the two using a serial interface, or via Bluetooth (I'm guessing you'll either need a Bluetooth shield or something similar). There are many resources on the Internet dealing with setting up Arduinos with both of these.
You may also be able to set up some sort of basic server on the Arduino and be able to interface the phone to it via a console, or through a specially defined interface on the phone, or even a web based interface. There seem to be a fair few robot designs being controlled by Android/Arduino maybe have a look at these.
Without some more ideas about what you intend to do once they're linked it's difficult to be more specific, although if you root your Android phone you will be able to install a cut down version of Debian on it, and then you will be able to apt-get install various packages. With this in mind, there becomes little difference between connecting your Arduino to a computer and connecting it to your Android phone.
[EDIT]: If nothing else you could make an Arduino based one of these: Android Controlled Statue.