A lesser known feature of Firefox, is its facility to allow the user to write custom CSS and have it apply to particular websites.

userContent.css resides in your Firefox profile, under the chrome directory.

Open it with a text editor and you can play around.

Here’s a few very basic alterations for the new Twitter:

@-moz-document url-prefix("http://twitter.com/") {
    
    //hide promoted tweets, and the favourites & lists areas in the sidebar
    .promoted,
    .favorites-activity,
    .lists-activity {
        display: none !important; 
    }
    
}

I’ve played around with a few other things but it looks like they’re using JS to set the styles of various bits and pieces, and I really can’t be bothered looking into Greasemonkey for it.