How can I fork my own GitHub repository?

You're doing the right thing.

cd ~/Sites/
git clone ~/Dev/markupDNA/ project-N
cd project-N
git remote rename origin markupDNA

• Nav to the folder where you store your projects
• clone your base markupDNA repo with custom name
• rename the remote so that if you want to an 'origin' later, you can

It will probably be a lot easier to use branches, rather than using separate forks. You can still have separate checkouts for each branch; just clone your repo multiple times, and use git checkout in each one to switch it to the appropriate branch (or git checkout -b to create the branch and check it out all at once). Once you have created the branches, you can push them to GitHub using git push origin <branchname>.

This tutorial gives a simple and straightforward answer :

1. Create a new empty github forkedreporepository

2. Clone it locally:

   git clone https://github.com/YOURUSERNAME/forkedrepo.git
   

3. Add the original github repository as remote of the new local repository:

   git remote add upstream https://github.com/YOURUSERNAME/originalrepo.git
   

4. Pull down a copy of the original github repository to your new local repository:

   git pull upstream master
   

5. Push the files from your new local repository to new github repository:

   git push origin master
   

This won't be recognized by github as a fork of the original repository, off course, but this is as good as it gets.