Add the remote, call it upstream:

git remote add upstream https://github.com/slatedocs/slate.git

Fetch all the branches of that remote into remote-tracking branches, such as upstream/main:

git fetch upstream

Make sure that you're on your main branch:

git checkout main

Merge our updates into your main branch:

git merge upstream/main

Push the updated code to Github:

git push

Update installed gems (if using slate natively):

bundle install

Publish the new changes to Github pages:

./deploy.sh

(Thanks to Mark Longair on StackOverflow for the upstream explanation.)

If using Slate under Vagrant or Docker, you will want to destroy and rebuild the Slate image for it, using either vagrant destroy or docker rmi slate while in the slate directory, and then re-running through the instructions on those pages.