Yosemite and later used a built in program called createinstallmedia to automagically make a USB stick. It is possible to create a bootable USB stick without this program.
You'll need an 8GB USB stick and either the Install Mac OS X Lion.app or InstallESD.dmg or BaseInstall.dmg.
Open Terminal, you'll need it in most of this tutorial.
We're going to need to start by getting to the actual installation disk image.