OK, I use sponge daubers like these shown below. You tap them on your ink pad, then on your project. They're pretty small, so the ink should stay on top of the embossing.
To ink the folder, you can either use a brayer to pick up ink from an ink pad then roll it on the inside of the top part and the ink would not go in the holes, so the raised part would be the paper color and the non-raised part would be the ink color. Or you can put ink in the holes and wipe it from the rest of the folder. That would put ink on the raised parts and not on the flat parts.