If you understand the work of Jean-Auguste-Dominique Ingres, you also must understand that truly replicating his painting techniques would be nearly impossible. This is not because Ingres had tools unavailable to modern painters, nor is this because his skill with the brush is so much greater than what could be possible today. It is because his paintings are so much about the subjects he painted, and his subject matter was so deeply entrenched in his own period in history.
Modern or Historical?
After studying the works of Ingres, you may ask yourself whether it was more important that he painted fashionable women of his specific time or that he painted fashionable, contemporary women. If you are trying to replicate his technique, is it more important to paint women who were contemporaries of Ingres--or women who are just contemporary.
If Ingres were alive today, there is no way to say if he would be painting with a similar style and similar subjects---in fact, he would very likely not. However, for the sake of argument, had he continued on the same trajectory he was on when he died in 1867 (without growing or changing significantly as an artist), he would be painting the wealthy elite of today.
Ingres also made paintings with classical themes, often involving nude, eroticized women that, if painted in a similar presentation today would likely make Ingres the target of passionate criticism from feminist groups.
To replicate his technique, paint a lot of portraits, mostly beautifully dressed women. Some of them will be more virtuous in appearance than others. Dress them gorgeously. They should be wearing expensive, modern, visible jewelry. It should be obvious that they are indeed rich. Pay close attention to the clothes and the styles. Your portrayal of their fashion, the textures of the different materials, the threads in their clothes, the buttons and shoes, all should be flawless. Your painting should appear so real that it nearly looks more real than the reality. The setting for your subjects should be modern rooms where they would naturally reside or flat backgrounds of no specific location at all.
Medium
Ingres used oil paints on canvas. He detested the presence of brush strokes on paintings. He rendered his paintings as if they were windows into a softer and more beautiful world than what he existed in. It looked almost realistic, but idealized and perfected.
Use oil paints. Use hard lines when called for, but, when blending, blend perfectly. Leave no evidence that you are painting at all.
Color
Ingres used rich, beautiful colors and earth tones. Most of his paintings had warm tones overall, allowing the presence of cooler colors to stand out. If replicating his style, paint with browns, reds and yellows. Use cooler colors somewhat sparingly, but do not shy away from them. Instead, reserve them for special items in the canvas.
