To create a copy of an existing test plan,
1) Click on "Your Plans."
2) Search for the plan you want to create a copy of.
3) Hover to the right of that plan name to pull up the 3 purple tool tips.
4) Click on the "copy" icon as shown below to create a copy of the plan.
Select Plan Name and Project
Input the name for the new test plan and select the project to put the copied plan into. You can create a new project by selecting "Create a new project...," and typing the name on the popup screen.
A couple of things to note:
"Plan name" of the copy will just add "(copy)" to the original by default, but can be changed as long as it is unique in a given project or the private collection.
Project name has to be filled and should be unique per user account (i.e. another user can have a different project with the same name).
"Revision History" checkbox allows to preserve traceability of edits across plans. However, for old plans, it may be better to clear the history for faster performance.
"Switch" checkbox allows to instantly start working on the copied version. Uncheck it if you create something for the future needs and are not ready to edit it yet.