It seems that it is not easy to find a reference containing a classification and construction of finite dimensional irreducible representations of $GL_n(\mathbb{R})$. One way to look at it is via $(\mathfrak{g},K)$ module, and we do have a classification theorem in terms of highest weight, but it is not obvious to get the explicit constructions from this,especially in higher rank case.

So I'm wondering is there some good reference containing explicit constructions of all irreducible finite dimensional representations of $GL_n(\mathbb{R})$?