I think the most common way is to make your way to that problem editor (say by finding an existing problem and clicking to edit it) and then clear the screen (or perhaps clear most but preserve structural elements). Then understanding the View, New Version, Append, and Revert tabs becomes important. You could use the New Version tab to define a file path and name for your new file. And after that, either use the View tab to compile the problem without saving, or keep using the New Version tab. Either way, clicking "Take Action" compiles the problem in a new tab.
(Append is like New Version, but adds the problem to an existing set. Revert is for when you have used View already, thereby creating a temporary file, and you want to trash that and go back to the last permanently saved version.)
If you edit from the server with your favorite text editor, you could separately view the output in a web browser as follows. The file should be in some course's templates/ folder (or have a file path within the templates/ folder). So for example:
vim /opt/webwork/courses/mycourse/templates/myproblem.pg
Then with a web browser, use an address like this:
https://webwork.mydomain.edu/webwork2/html2xml?&problemSeed=1&answersSubmitted=0&sourceFilePath=myproblem.pg&displayMode=MathJax&courseID=mycourse&userID=myuser&course_password=mypassword&outputformat=simple
In that URL, you should customize:
webwork.mydomain.edu
myproblem.pg (this could also be a file path like myproblems/myproblem.pg)
mycourse
myuser (some user account with at least login_proctor permissions)
mypassword (the password for that user)
Note that I would avoid using your actual professor level user account and password for this, since it would be too easy for that URL to accidentally be sent to a colleague or something, and you forget that it reveals your password.