Use the Save Report button in the lower right corner of every report to access the Save, Share, Description, and Schedule options.
Saving a report includes the report in your Report Menu in the top menu. You'll see the report in the drop-down, fly-out menu of the global report navigation.
There may also be an option to save as new report if the report you're using originated from a previously saved report.
"Save as new report" will save a new report without overwriting any changes you've made to the previously saved report.
Saving as new does not force a name change to the saved report, but it is always a good idea to change the name anyway so that you do not have two different reports with the same name.
If the report you are saving was shared to you by another user as the original report creator, the save as new report option is the only option available. You cannot make and save modifications to a report created by another person, but rather you will save your own new report.
The Description tab is meant to help you organize your report. Descriptions help explain the purpose of the report in more detail than you would normally include in the report name.