You can upgrade the Site Studio module using composer or manually. 

Step 1a - Upgrade using composer¶

Using composer is the preferred way to upgrade Site Studio. 
It is not recommended to edit the composer.json file manually.

Open your terminal and browse to the directory containing your project root directory. Run the following commands, updating the version number to the version you want to update too:

composer require acquia/cohesion:6.0.1
composer require acquia/cohesion-theme:^6.0

This will then update your Site Studio module and Acquia Cohesion minimal theme to the version you have set.

Step 1b - Upgrade manually¶

Upgrade Site Studio module¶

Navigate to the download page for the module: https://github.com/acquia/cohesion/releases and click "zip" or "tar.gz" on the top entry to download the Site Studio module. 

Once the file has downloaded, unzip it, rename the folder to "acquia-cohesion" and then copy to your /modules/contrib/ directory of project. When prompted click "replace" to replace your older version of Site Studio with the new one you just downloaded.

Upgrade Acquia Cohesion minimal theme¶

Navigate to the download page for the theme: https://github.com/acquia/cohesion-theme/releases and click "zip" or "tar.gz" on the top entry to download the theme. 

Once the file has downloaded, unzip it, rename the folder to "acquia-cohesion-theme" and then copy to your /themes/contrib/ directory of your project. When prompted click "replace" to replace your older version of the Acquia Cohesion minimal theme with the new one you just downloaded.

Step 2 - Run drush commands¶

Next, you will need to run a few drush commands, open up your terminal and browse to your project root directory. 

First, you should clear your website cache.

drush cr

Next, you will need to do a database update. Running this command will apply database updates to your Drupal site that the new version may require.

drush updb -y

Then finally you will need to do a Site Studio import and rebuild. 

Using drush 9:

drush cohesion:import
drush cohesion:rebuild

Using an earlier version of drush:

drush cohesion-import
drush cohesion-rebuild

Once Site Studio has finished running the import and rebuild, your Site Studio version will now be up to date with the version you downloaded.