Here is a 12 step method I came up with after rooting my droid x today. A computer is not involved in any of the steps. Enjoy!
1. Press the menu key on the bottom left part of your phone (looks like 4 squares)
2. Select settings
3. Select applications
4. Take a look at the unknown sources option and make sure the box is checked (this enables installation of non-Market applications)
5. Using your phone, press your finger on this link: Hotfile.com: One click file hosting: z4root.1.3.0.apk
5. Click the regular download square
6. Once the download is finished, press the menu key
7. Select notifications
8. Select the z4root icon and accept the installation
9. Select the apps launcher icon on the bottom of the screen (looks like a triangle in a circle)
10. Select the z4 app
11. Click the permanent root box (you will have the option to un-root or re-root once you have root)
12. If successful, the black screen with the moto M should come up. You may need to remove the battery to reboot your droid x. When the phone reboots, a prompt will ask you to allow superuser permissions. Congratulations, granting superuser permissions means you will now have root access. Superuser will now be available in your app library.
This method worked for me. My droid x had a 2.2.1 Android version and 2.3.340 System version. I would like to share my success with the forum. I do not take credit for the information shared. But I did take the time to put this 12 step process together for others to read.
I was once afraid to root. I was worried about bricking my phone after reading some of the threads on this site. Do your own homework. Rooting is quite safe. However, I will not be able to help you if you have any problems. With that said, here is what you will be getting yourself into:
Rooting is a process that allows users running the Android operating system to attain privileged control within Android's Linux subsystem, overcoming limitations that carriers and manufacturers put on such phones.
Comments and suggestions appreciated. Thanks
Edit: My Android version was 2.2.1 before rooting not 2.2. This has been corrected.