How to learn the basics the right way?

I'm 1300 rapid. I always make very basic mistakes like moving a piece leaving another piece hanging, or not being able to visualize how the board looks after a few moves or exchanges causing wrong calculations,etc. Most of my mistakes are based on terrible calculation in general.

I think I lack the fundamentals of chess because I learned in a non-organized way collecting random information from here and there and just playing.

How do I learn the fundamentals the right way? What advice do you have for me?