16.04unitywindowwindow-manager
I recently purchased an ultrawide monitor, and I'm using it with Ubuntu.
Unity comes by default with a way to snap things into the corners or half the screen, but I'd like a to be able to split my screen into 1/3s side by side. Also, in general I'd like to be able to customize the snapping easily, so I could change to say, four apps side by side if desired.
I've looked but It doesn't seem like a common issue and thus, there are few tutorials on it.
Does anyone know how this can be accomplished?
Yes this is possible. If you use CCSM, you can configure the "grid" plugin to include all the corners of the screen and even the bottom edge of the screen.
Click below to install:
Then:
The level of precision you seek is not available. You said in a comment "without having to drag" (please don't expand the scope of your question in comments ;)) though, and this can be done with keybindings.
As you've found out, Ubuntu 18 has moved away from the Unity desktop manager which I had finally gotten used to, to Gnome desktop, which is much different. Compared to Unity, Gnome Desktop's configuration settings are all wacky. You'll need to install Gnome shell extensions.
I recommend using the Put Windows GNOME extension, like @heynnema says.
However, hknust likes the ShellTile one, so you can try it out too.
Note that Gnome Shell extensions change how your desktop works, but you configure them through your browser, which seems kind of weird at first. Your browser, in this particular case and for this particular application, acts as a front-end messaging service to communicate with the back-end configuration settings which apparently are running as a background program on your PC.
Steps (in part borrowed from hknust's answer):
Enable shell extensions (the back-end service) on your PC, and the Gnome shell extension in Chrome (the front-end configuration panel):
sudo apt install gnome-shell-extensions chrome-gnome-shell
In your Chrome browser, open https://extensions.gnome.org/.
Search for "put windows", as shown below, and click on it. 
Install it by clicking the button to the far right of it. You may see a message saying you need to install "GNOME Shell integration" from the Chrome Web store. If you do, go here and install that into Chrome: https://chrome.google.com/webstore/detail/gnome-shell-integration/gphhapmejobijbbhgpjhcjognlahblep.
Now you'll get that little foot-icon extension in the top-right of your Chrome: 
. Click it, then click the "Installed extensions" tab at the top of the page that loads. You'll now see the "Put Windows" extension installed as shown here. Note that you may need to refresh the page to get it to show the screwdriver and wrench icon once you've installed it: 
.
Configure it by clicking the little screwdriver and wrench icon under the yellow arrow I made in the image above. Notice the default keyboard shortcuts are set like so: 
Super (ie: Windows key) + Keypad 7, for instance, will tile the selected window to the top-left corner of your screen.
) in the top-right of your browser --> Find your "Put Windows" entry as shown here: 
, and click the "ON" slider to toggle this extension off, then click it again to toggle it back on. Now try your Put Windows window snap shortcuts and it should all be working! Alt + Super + S and the other shortcuts should all work fine now.BUG NOTE/WEIRD BEHAVIOR: If you are trying to snap a window to a corner but its size is off, first snap it to the center (Alt + Super + S), then snap it to the corner (ex: Alt + Super + Q to move to upper-left corner), and it will now be the right size to allow 4 windows to be seen at once--one in each corner, as snapping it to the center first also gets it to be the right size--ie: exactly 1/4 of the screen area.
Done!
Best Answer
For managing multiple apps/ windows, it's always good to use a tiling window manager instead of the regular desktop.
Tiling window manager Wiki
Consider trying, Awesome Window Manager
Very much customizable, guaranteed improvements in productivity.
Here is the Overview youtube link.