Here are a few options:
This seems to be the standard reference for Real Algebraic Geometry. Most of the chapters(at least the first 5) should be accessible with a bit of work. Later chapters will require a bit more background.
This gives an overview of some of the ideas behind real algebraic geometry. It starts by defining what ordering of rings are and how they connect to geometry. Moves on something called the real spectrum of a ring together to results related to it.
This is one my favorites intro papers. It is clearly written and presents the material well. It is a bit dated but I like how it treats the Real Spectrum. Might be a bit too advanced, specially if you have never seen scheme theoretic approach to algebraic geometry.
Not sure if this is an intro to the subject but it gives a quick overview of semi-algebraic and real algebraic sets and discusses some topological ideas related to it. For example, how in low-dimension we can characterize real algebraic sets.
Semi-algebraic geometry is often used as a synonym for real algebraic geometry. This gives you a quick intro together with some of its computational tools.
Similar in spirit to the above, but a lot more comprehensive. Contains a lot of the background material.
You might not be find a complete linear path to learning geometry. I am not sure if this is 100% sound advice but just get stuck in. If you then find some material which you haven't encountered you can take a small detour.