I would suggest copying the files from Portals/_default/Skins/DNN-Gray to Portals/[your portal ID]/Skins/DNN-Gray
Then, open the HTML file for the skin you want to edit from the new directory in whatever HTML editor you want to use (I suggest Expression Web).
You can edit the code and view an approximation of the result while you're editing. When you're done, save the skin then from the Admin | Skins page, unselect the checkbox that says 'Host' and select your 'DNN-Gray' skin from the drop-down box. Then scroll down and click on 'Parse Skin Package'. After that, select 'Preview' under the skin you just edited.

You can keep repeating that- edit the skin, parse, preview... until you get the skin looking like you want.

Also, if you rename the folder the skin HTML file is saved in, that folder's name shows up as the name of your skin.