How to maximise a window to fill up screen in Mavericks?

For maximizing windows (and more), I use SizeUp: http://www.irradiatedsoftware.com/sizeup/

This is not the same as full-screen mode which Mark refers to.

While holding Shift + Option, click the green Plus button on the upper-left corner of the window.

Option + click on maximize button works for me.

I have been using SizeUp but recently I heard of Spectacle:

which seems to do most, but not all, of the same things, and is free and open-source.

What you can do is make an app go full screen. This is done by hitting the double arrow icon at the top right of the window (see picture below) or the keyboard shortcut ^+⌘+F.