How do I update the browser on my iPad?

Safari browser come natively installed with iOS. To update the browser, install the latest updates for iOS 13.

Go into Settings > General > Software Updates --follow the on screen instructions

Update your iPhone, iPad, or iPod touch - Apple Supportsupport.apple.com › en-us

If you are talking about Safari, it updates automatically when a new iOS version is released. There is nothing you need to do to update it.