Ravi Vakil's The Rising Sea: Foundations of Algebraic Geometry is an excellent textbook on (you've guessed it) foundations of algebraic geometry, very nicely mixing rigorous proofs, intuitive explanations and illustrations. It is available for free on author's website, and the newest version (along with all other versions) is always available here:
There is also Fulton's book Algebraic Curves: An Introduction to Algebraic Geometry is another nice book whose latest edition has been published for free by the author. It gives an elementary introduction to the theory of algebraic curves, up to desingularization and Riemann-Roch theorem.
Both books require some familiarity with abstract algebra, but assume no prior contact with algebraic geometry.