How do I update the browser on my iPad?

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.

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