I do not know that tutorial, but i can summarize the things you need to know.
A Button is 64x64 pixels small, should be saved as DXT3 .dds file, and must have MimMaps turned OFF (to avoid them appearing extra-blurry in some UI elements).
To make it match the original look, you would have to paste a copy of the frame from an original button on top of your image.
The rounded corners in default Civ4 Buttons are done via alpha channel - making the corners invisible.
Attached is my template with already pre-set alpha channel, frame layer and a selection of original Civ4 unit backgrounds, that might help to speed up the process - just enable the background that fits your need and paste your image into the empty layer below the frame. To improve the overall result, you can apply a pass of unsharp mask (~3px wide, medium intensity) to the image layer only (not to the frame/bg layers).
You can use it with Photoshop or Gimp (maybe other graphical software capable of working with multiple layers as well).