If you're looking to install the Public Beta of macOS Sierra on an external SSD, this is how you do it.
It's what I like to do because since it is a beta, there will be bugs and sometimes things can go wrong. Installing a beta, whether public or developer on a stable production system isn't a wise thing to do especially when you have critical services or files on the system.
Even though I keep up to date Time Machine backups, I still take this extra step of installing betas on a separate drive. If something goes wrong with it I don't have to worry about losing anything or more importantly I don't worry about taking time to restore from a backup to my stable system. All I have to do is reboot the Mac from one OS to another and I'm ready to go.
What I recommend is that you use a decent SSD, I prefer the Samsung 850 EVO, and quality USB 3 enclosure like the Inateck 2.5 drive enclosure. I like this enclosure because it uses a full and standard USB interface on both ends of the cable. I've had other enclosures that use a micro USB connector on the enclosure side and they're usually flimsy and always feel like they're going to come out.
Also I recommend that you use a good USB flash drive for this process too. I like the Kingston Data Traveler in 32GB and USB3. This one ensures you have plenty of space available and you get the higher speed data transfer too. Although as a minimum, a USB 2 flash drive with at least 8GB of space will do; it will just be slower.
Once you get the gear you need go into your Apple account for the beta software, https://beta.apple.com/sp/betaprogram/ and follow the directions to enroll and download.
Once the download finishes, do not install it. Rather cancel it and make sure your USB flash drive is connected, open Terminal and enter the following command:
sudo /Applications/Install macOS Sierra Public Beta.app/Contents/Resources/createinstallmedia --volume /Volumes/Untitled --applicationpath /Applications/Install macOS Sierra Public Beta.app --nointeraction
From there enter your password and follow the prompts.
Once that is done you can reboot your Mac, with the external SSD connected and turned on if it has a switch, while holding the Option button on the keyboard. You should see the USB installer in the list and then click on that to run it.
Follow the prompts and when you get to the part where you choose which disk to install it on, be sure you select the external USB SSD. If you choose your internal drive you will overwrite your good installation. Always be sure you have a good backup prior to starting this process just to be safe.
Happy beta testing!
Download the pdf version with pictures here.