In order to separate colors in Photoshop, you must create a new canvas with the size being the exact print size or larger, 300 - 600 resolution, and set the color mode to CMYK.
Once the artwork has been opened, your first step should be to duplicate the layer by right-clicking on the layer in the layer box and selecting “Duplicate Layer.” This will ensure that the original remains untouched in case of mistakes or dissatisfaction with your results.
Once you have a duplicate layer, the next step is to separate one of the colors from the artwork. In order to do select the color you want to separate, you will need to use the magic wand tool. The magic wand tool allows you to grab a color within a trapped area, which is controlled by the “tolerance.” The higher the tolerance, the more color/shades of color the wand will select. It is extremely important to set the tolerance at the right value before using the magic wand tool to select a color.
Once a color has been selected, you must cut and copy it to a new layer. To do this go to Layer>New>New Layer via Copy (command+shift+J (Mac), control+shift+J (Microsoft)). New Layer via Copy creates a new layer featuring the selection made from the magic wand tool and removes the selection from the original layer.
Once the first color has been removed, the layer must have a “color overlay” applied. To apply a color overlay, double-click on a layer to open the “Layer Styles” window and go down to “Color Overlay.” Click on the color box at the top of the screen and the “Select Overlay Color” box will open. Change the C, M, and Y values to 0 and the K value to 100 and click “OK” in both the “Select Color Overlay” and “Layer Styles” boxes.
Remove any other color(s) from the original layer through “New Layer via Copy” and then apply a color overlay. Once all of the colors have been separated you will need to turn off the original layer that you pulled the colors from and make sure the original duplicate layer (has all colors within the design) is turned on. This original duplicate layer will be used as one of the separated colors and help fill in the gaps where the colors are not touching. Simply apply a color overlay over the duplicate layer and make the values of CMYK all 0, except for one of the colors (must be different than the other separated color(s)).
Separating colors in a bitmap program like Photoshop does not work as smoothly as a vector program like Coreldraw or Adobe Illustrator, but will work if the artwork is simple and high resolution.