The steps I describe below are done with Adobe Photoshop. Other image editing programs could do this, but I frankly do not know the steps for those programs.
After the three separation negatives are each scanned to individual files, they are assembled as separate layers in a single Photoshop document, each separation layer labeled according to its corresponding color: RED, GRN, and BLU.
The images are inverted to a positive. If you use the Photoshop actions I have provided (available to registered users on the Knowledge page of the PERMANENCE project), you can correct density and color before combining the three images as a new composite color document. Now I'm sure it's not intuitive to you how to correct color while working in black-and-white, so you will find further explanation for this topic on the Knowledge page.
In Photoshop, the positives layer document will not look like the images in the picture below, as they are still black-and-white. Just know that when you run the action to combine them into a new composite color (RGB) document, Photoshop internally reverses the colors as well: when RED is reversed it is cyan, GRN reversed is magenta, BLU reversed is yellow. That's why the positive images are displayed below with inverted colors. (The more astute readers might ask why are the channels labeled "Red", "Green", and "Blue" in Photoshop if they represent colors in the reversed shades of cyan, magenta, and yellow. This is a more advanced topic - which I'm happy to blog about, if there is interest.)
With the black-and-white layer document still open, the action creates a blank color (RGB) document, then peforms three "pastes": the RED positive black-and-white image layer is pasted into the blank color document's Red channel, the GRN positive black-and-white image layer is pasted into the blank color document's Green channel, and the BLU positive black-and-white image layer is pasted into the blank color document's Blue channel.
Then - voila! - You have a color composite, as the example "Finished Print", below. You may not consider it finished, so you can do further corrections to the composite itself, or go back to the layered separations document, make more corrections, and redo the composite.