Next, go to the z4root forum page.(http://goo.gl/ormoU) on xda-developers.com and download the latest version of z4root to your phone. NOTE: If you are having trouble downloading the file directly to your phone, it's likely due to a bug in the default android browser for Android 2.2 (Froyo). Try using an alternate browser like Firefox or download the file to your PC and copy it to your SD Card.
Once z4root has been downloaded, open up the Astro app on your phone and locate the z4root apk file. If you downloaded it on your phone's browser, it should be located in your Downloads folder. Otherwise, it will be on your SD card wherever you copied it.
Tap on the file. Then tap on Open App Manager.
Now you can tap on the Install option for z4root.
Now that z4root is installed, go ahead and launch it by tapping on Open.
You'll now see options to do a Temporary Root or a Permanent Root. Tap on Permanent Root.
The phone will begin running the exploit scripts in order to root the phone. Leave the phone alone at this point. The rooting process will take a few minutes and will end with z4root rebooting your phone.
NOTE: If the phone freezes for more than 5 minutes while Running Exploit, don't panic. Just pull the battery out of your phone, pop it back in, restart the phone and try again.
You're done! If you launch z4root, you'll now have two options: Re-root and Un-root. That shows you successfully rooted your Droid 2 phone.
Have fun tinkering and exploring your newly rooted Droid 2.