Basically, apt-fast is a script that use axel to download deb files that are needed before the process of actually doing apt-get.

axel is a download accelerator that the command is run via the terminal. Many users use axel to replace the use of wget.

Here's how to install and use apt-fast

1. first off all, install axel
sudo apt-get install axel  
2. then download apt-fast.sh here
3. Rename apt-fast.sh to apt-fast by remove ".sh" extension
4. Move apt-fast to /usr/bin/, if you don't have super user/ root permission, U can  
    use this way, read here
5. Create apt-fast file into executable file:
sudo chmod +x /usr/bin/apt-fast

After the above steps done correctly, please try using apt-fast in the same way when you use apt-get and feel the difference

For example:
sudo apt-fast update & & sudo apt-fast upgrades


good luck