Q: How do I upgrade my browser?

If you are using OS X 10.7.5 as your signature indicates, the last version of Safari for that was Safari 6.1.6

You would upgrade Safari by upgrading to El Capitan OS X 10.11.6

If you cannot or don't want to upgrade to El Capitan, one option is to download and use Firefox instead of Safari. https://www.mozilla.org/en-US/firefox/new/

The current version of Firefox (47.0.1) is still supported for OS X 10.7.5 but that will also be discontinued soon. See https://blog.mozilla.org/futurereleases/2016/04/29/update-on-firefox-support-for -os-x/

See if your Mac meets El Capitan v10.11 requirements >  Upgrade to OS X El Capitan - Apple Support

With El Capitan installed Safari would be updated to version 9.1.2 the latest version available.