The nicest source that I know is Hasse's Zahlbericht (originally published as Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper in 1930 and republished in 1965), the first part of which gives the ideal-theoretic approach with Takagi's proofs, and the second part of which gives Artin's reciprocity law along with many charming explicit reciprocity laws. The original papers of Takagi (available in his collected works) are also readable. Herbrand wrote a nice summary of the state of the art in 1935 (Le développement moderne de la théorie des corps algébriques; corps de classes et lois de reciprocite (Mem. Sci. Math. 75) Paris: Gauthier-Villars. 72 p. (1935)), which is available in most university libraries.
Lang in his Algebraic Number Theory (originally based on lectures of E. Artin), in fact, follows the original proofs fairly closely, although he uses ideles and the Herbrand quotient to streamline the proofs. One can get a sense for the sort of simplification that ideles afford by reading Franz Lemmermeyer's article on the development of genus theory (in The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae Springer (2007) or at Lemmermeyer's own web page). In that article Lemmermeyer discusses the history of the famous first and second inequalities from their original appearance (with algebraic proofs that, in a sense, reappeared in Chevalley's treatment of classfield theory) in Gauss's Disquisitiones through their 19th-century Dirichlet-style analytic treatment and to the form used in the classfield theory of the 1920's. Since Lemmermeyer (following the historical sources) works with full rings of integers (without any idelic techniques), there are many tricky local terms in the formulas. Perhaps that is what you're hoping to see!