Well, you could create a separate report for that one page and share it with only the people that need to see it. Or, you could use RLS in the existing report. But, you cannot add secrurity to a page like what I think you are asking. You can hide it, but that's not really security and it is hidden for everyone.
So, in the Service, in the left nav under My Workspace, if you scroll down to DATASETS and click on the data set in question you should be presented with a blank page. You should then be able to start clicking fields to create visualizations on that page and then use File | Save or Save As to save it. What piece of that is missing for you? Is this a data set that you created and uploaded?