Customizing Log in Widget

How can you go about customizing the login widget? I don’t want to change any functions, I just want to move the links, buttons, etc. around (css stuff).

The default setup has the username box on top of the password box, and once you log in it is the list of links next to it. I want to essentially make it horizontal, with the two boxes side by side instead of stacked, then once you log in it will just be the links (log out / dashboard), possibly a welcome message too, but that can come later.

Help is sincerely appreciated! I have been playing around with this for quite some time and have hit a wall