Laravel default app (https://github.com/laravel/laravel.git) doesn't change much and when it changes, Taylor gives the steps to migrate it. What you really want to do is to keep your project in sync with https://github.com/laravel/framework.git, for that you just have to
composer update
Every day.
But if you really want to have default app in sync too, here are some steps:
1) Go to github and fork https://github.com/laravel/framework.git.
2) Install your application as you would normally:
composer create-project laravel/laravel your-project-name --prefer-dist
3) Rename git origin to anything else:
git remote rename origin laravel
4) Create a new project on github and add it as your new origin
git remote add origin https://github.com/you/yourproject.git
5) Add, commit and push it:
git add -A
git commit -m "first commit"
git push origin master
And you should be good to go.
Every time you need to merge yours with Laravel's you'll probably need to:
1) Fetch the changes
git fetch laravel
2) Take a look at the list of branches:
git branch -va
3) Merge yous with laravel
git merge laravel/master