[Motorola Droid 3] apefist:
Hey, so this was my process.

First, I made sure that the stock software on the phone was up to date. I did this since that way if you have to go back to stock, you are on the latest version, and you can confirm that you are using the correct rooting application. The root tool I link to below will work on 5.7.906 which I believe is the latest.

Second, root your phone. You will need to go HERE to download the tool. Follow the instructions on the page, and it should go fine. The phone will reboot several times during the process, this is normal. Once the program says it is done, you can go check for the Superuser application in your app drawer (it might be SuperSU or something similar, I can't quite remember).

After you have root access on your phone download the safestrap application for Droid 3 HERE. Make sure you get the one that is specifically for Droid 3. Transfer that file (should be called Droid3Safestrap-3.05.apk) onto your phone.

There are a few ways to transfer files onto your phone. You will also need to do this later to transfer the .zip of whatever ROM you decide on). If you have a micro-sd card that you can put into your computer, that works. Or, you can have the phone on and plug it into the computer and transfer it that way. I believe you can transfer to either the micro SD or the internal memory. I prefer micro SD since you might want to wipe the internal memory to fix things or switch ROMs.

After the .apk is transferred find where you put it using a file manager (I personally use Root Explorer but I think Astro or stock will work), and install it. Go to the new app and run it and it should request root access, which you grant, and it should flash the recovery.

Once you have the recovery installed you can install whatever custom ROM you want, pretty easily. Safestrap is great because even if you screw up the ROM somehow, you can always just boot back into Stock.

Here is where you'll have to chose what custom ROM you want. Now as far as I know, the Droid 3 is fairly limited in its ROM selection. It does have a Cyanogen Mod 10 version, but it is not a stable version and in my experience, doesn't run super great. If you want to try Cyanogen Mod 10, I actually suggest you get the Avatar Rom variant HERE, but keep in mind that apparently you do need a SIM card inserted for the cell signal to work at all. Overall it did seem to run fairly choppy but they are still releasing newer nightly versions (July 20th was the last) so it might have gotten better. One thing to know about these ones is that the camera does not work at all, so if that matters to you just skip these.

Now those two (CM 10 and avatar) are ROMS that will bring the droid 3 up to Android 4.2 Jellybean. If you don't care about getting up to the latest version (Jellybean actually isn't the latest anymore but still pretty darn close), then there are a few other Gingerbread ROMS out there that work a bit better.

HERE is a list of a few other droid 3 ROMs, my favorite Gingerbread one that worked overall really well and stable was Steel Droid. Otherwise, you can just look around and see what's available or what other people are suggesting. Choose your ROM (or several, it's fairly easy to install them so try a few!), and download it. You should get a .zip that is approx. 150-170 MB in size. As an aside you will probably also want to download the corresponding GApps package HERE and put that on the SD card as well. I think some ROMs have that included, but if you boot into a room and it doesn't have the Play store installed, you need to go back into safestrap and install the GApps package over it. You don't have to delete and recreate the rom slot, just go back into install and install it over. When I say corresponding, the different packages go with different versions of Android so for example the one labelled 20110307 would go with Android 2.3.4 which is Gingerbread, the version that Steel Droid uses.

For whichever one you choose, the install process is mostly the same. Reboot your phone, and after the Motorola Logo comes up, you should see the Safestrap splash screen. To get into the recovery menu you have to hit the "Menu" soft-key (the one all the way on the left) within 10 seconds so keep an eye on it.

From the recovery menu go into "Boot Options" You should see 5 options, rom-slot 1-4 and Stock. When you want to switch what ROM you are booting you select on the corresponding slot, and hit activate, then you can reboot through the menu option and it will start that ROM.

To install you will go into "Boot Options" chose whichever rom slot you want (most likely #1). You will have to create that slot, which can take a few minutes. After the slot is created, back out of boot options, and go to "Install". Find the .zip of whichever ROM you chose, and select that to install, and then you can install the corresponding GApps package.

After the install is complete, you can reboot (make sure it says rom slot 1 is selected up to), and it should boot into the Setup process of the ROM. If you ever need to go back to stock, just reboot, go back into Safestrap > Boot options, activate the "Stock" one and boot into that.

A few notes, if you want to switch ROMs, or install multiple ROMs you can do that using the different rom slots with a few exceptions. The Cyanogen Mod 10 and the Avatar Rom (most Jelly bean ones I think) have to be installed in rom slot 1, so if you're doing those and another like Steel Droid, put the Jellybean one in rom slot 1 and the Gingerbread on in rom slot 2. Also if you want to install a different ROM, it's generally best to just completely erase the rom slot and recreate it, then install the different ROM in the newly created rom slot. You can always create backups with Safestrap and restore them with Safestrap. Oh and make sure your phone has a decent charge before doing a lot of the safestrap stuff (I would say at least 60%) you can also have the phone plugged in while doing this stuff, but I'm not always confident it is charging so try and get it charged up before hand.

Finally, if you ever mess up to the point where you're worried that you broke the phone, (boot loops or it is stuck on the Motorola Logo) you can download this restore tool HERE. This should completely wipe and restore the stock software on your phone. It will bring it back one version previous though, so be sure to go through the standard update process to bring it back to 5.7.906 so that the root tool will work. This tool has saved me a few times and is pretty easy to run.

Sorry, I know that is a lot of stuff and looks pretty scary. It really is just a few steps that you should research and make sure you are comfortable doing.

1: Get Root access on the stock software on the phone

2: Install safestrap and flash the custom recovery

3: Boot into recovery and install whichever custom ROM you want

If you have any questions feel free to ask!