To update between a minor version of Twill you can run the php artisan twill:update command. This will copy the javascript and css assets over to your public folder.
If you want to make it easy for you, you can add a post update action to your composer file to automate this every time you composer update (docs):
1"post-autoload-dump": [2 ...3 "@php artisan twill:update --ansi"4],Updating Twill between minor version (ex 3.0 to 3.1) should rarely require manual intervention as we do our best to keep backwards compatability.
For major updates we try our best to provide a seamless upgrade experience, but we cannot always handle every case.
When upgrading for example 2.x to 3.x make sure you check the upgrade notes in the repository or in the documentation page.