In order to turn a public UG tab into your Personal one, take these steps:
Click on Edit button
Choose Make personal edits
You're in editing mode now.
Edit/personalize the tab.
Click on the yellow 'Save as personal' button.
You can view your Personal tab in My Tabs section.
It will be marked with the human icon next to the song.
More details on where to find your tabs here.
Note: if you don't have an Ultimate Guitar account, it's worth registering one before you start creating the tab. This way you will not lose your Personal tabs.