To access the backend of LibAnswers go to
https://universityofcalifornia.libanswers.com/.
Login with your regular LibApps login/password (what you use for LibGuides, Appointments, LibInsight).
To practice with the chat feature, you may play the role of the patron and librarian, enlist the help of another UCI employee to act as the patron.
You can practice with the ticketing system asynchronously. Write yourself a question and then log in to LibApps to answer it.
Please include the word test at the beginning of your question to flag it as practice.