Step One is to enable debugging on the device under settings -> applications -> Development. Check the box that says USB debugging.

When you first plug the device into the computer and type: adb devices: at the command prompt, it will show up as a bunch of question marks, meaning that it won't work with the ADK.
In order to get it working you need to first get the usb device identifier. You can do this by typing lsusb into the fedora terminal application.
This will give you a list of usb devices plugged into the computer. You need to look for the one that matches your phone.
[paolo@svelt15 ~]$ lsusb
Bus 002 Device 006: ID 04e8:685e Samsung Electronics Co., Ltd
Next step is to create a new udev rule for the device using your favorite text editor. You can use vi or nano.
sudo gedit /etc/udev/rules.d/51-android.rules
then add the following rule:
SUBSYSTEMS=="usb", ATTRS{idVendor}=="04e8", ATTRS{idProduct}=="685e", MODE="0666"
Notice the produce and vendor ID come directly from the lsusb info above. You could use these instructions with other phones, in fact it worked perfect with my Nexus One when I was first developing on that.
After this is done you can either reboot or restart udev. Almost all of the instructions you find are for ubuntu but on fedora you restart udev rules with
sudo /sbin/start_udev Then just unplug and plugin the phone. It should now work with the ADK.
When you type: adb devices: You should now see the device listed instead of a bunch of question marks.
I havent even rooted this one, they barely lock it down now. In fact most the reasons I rooted my last phone are moot because this phone does them all: gingerbread and tethering. The only reason I probably still will is just so I can get rid of the facebook app.
Can you teach me how to root and completely hack my phone software someday? I would love to be able to do that!