All you will need is some kind of art program that allows you to draw with aliased brushes:

The software that I see recommended the most is aseprite, but if you don't want to / can't afford it, most art programs do have aliasing, so just do a web search on how to do that in your chosen program.
Use a 1px brush and start with something small. Maybe you can draw an object or a simple character. Try some simple shading and highlights. Then once you feel comfortable you might want to get into animating your pixel art pieces. Don't be afraid to use reference images or tutorials, just like any other type of art.