Distillation is carried out by using the equipment shown in the diagram below.
A simpler version that can be used in a lab is shown here.
You can follow the instructions here to carry out a simple distillation experiment yourself.
Is it possible to distill water at home? yes it is. look at some of the methods shown below. The first picture has a link to the website to explain what is happening.
A picture of a homemade distillation set up:
https://i.ytimg.com/vi/VPAKBxCIHAA/maxresdefault.jpg