Deligne's papers are probably not the introduction to classical Hodge theory you are looking for.

I would recommend reading "Hodge Theory and Complex Algebraic Geometry I" by Voisin. It covers the algebraic and complex analytic aspects of Hodge Theory, including sketches of parts of Hodge II. However, it skips the main analytic input of Hodge Theory regarding elliptic operators.

Prereqs: a first course in both differential manifolds and complex analysis first, along with the basic ideas of algebraic geometry.

"Principle of Algebraic Geometry" by Griffiths and Harris would be another good reference with similar prerequisites, although it doesn't cover more advanced topics such as mixed Hodge Theory.

"Period Mappings and Period Domains" by Carlson, Muller-Stach, Peters, might be an easier read - it has many exercises, and seems to have a greater emphasis on intuition and examples. It might skip some of the proofs covered in the above. I have not read it, though, so cannot vouch for it.