All traditional architecture is not necessarily classical. The classic is the very best of a tradition. Jefferson's Capitol would be an example of a classical building because it not only hearkens back to former classical buildings, but has itself become a classic. It is so because in it Jefferson took a previous example, namely the ancient Maison Carrée at Nîmes, and made it thoroughly modern for the new seat of provincial government in Virginia. In this example lies part of the answer to your question about the practical uses for classical architecture in the modern world.
Classicism is not un-modern. One of my professors in fact describes classicism as the "other modern." Modernism, the ideology that has held architecture around the world in a death grip since the 1920's, was based in the denial of all previous models and sought to replace them with the paradigm of the machine. The "international style" is a good example of such a mentality based in the desire for a new, unsullied architecture, fitting form to function. All but a few anachronistic modernists have long since left the machine slogan behind, however its influence can still be seen in even the tamest new construction.
Traditional architecture, on the other hand, seeks to work with and continue local traditions, to render the urban order of the city more intelligible, and to tell the user and passer-by about itself through its form. Part of this process involves the adaptation of the way things have been done in the past to suit current needs. In other words, it does what buildings have always done until roughly eighty years ago. In opposition to many modernist buildings which are often either completely inexplicable to anyone but their designer, or hideous blights on the land, (and more often both) the traditional building seeks to be a good neighbor. Being a good neighbor entails a willingness to have a dialogue with one's surroundings, not to be offensive, to understand one's place in the order of the city, and most importantly to contribute to the public good. This means that in a Western city such as Richmond, the provincial capitol will be the most important building, traditionally ornamented with a fully expressed order, etc., all at an appropriate scale. Lesser buildings take their cue from this and are ornamented in a way that tells the story of the city. Classical buildings like the State Capitol are the best of these good neighbors.
So, perhaps another question might be "what are the practical uses of an architecture that refuses to look to the past and continues to build indefensible, un-neighborly buildings?" Of course I have made this seem very cut-and-dry. There are many current architects who seek to use the modernist language in a communal, legible way, with varying degrees of success. I would argue, however, that such efforts are inherently futile.
I am not sure what exactly you mean by the resources and processes originally used, but your question does raise an interesting question: how do we recover the skills and traditions of a building craft ignored for the last half century? One of the main difficulties with such an undertaking is the difficulty of mastering many of the required skills of the traditional architect and builder. Many of these traditions have been protected or rediscovered in the preservation field. There are several institutions around the world, my school among them, which seek to continue and spread the skills and traditions of the last 2700 years.
If you would like to know more about traditional and classical architecture and urbanism I would recommend the book, Architecture: Choice or Fate, by Leon Krier. It is a great place to start understanding classicism in a modernist world.
Please let me know if you have any other questions.