Updating a theme is exactly the same as installing it anew. Have a look a our “installing a theme” article.
Once the new version is installed, you can navigate to Appearance > Themes and delete the old one.
After activating your new theme go to Appearance > Menus > Manage Locations and set your menu to be the theme’s main menu. Updating the theme will un-set it. Also, if you get 404 errors while trying to visit some of your posts, refresh your permalinks and the issue will be fixed.