The most commonly recommended covering for the cage floor is plain old newspaper.  It is inexpensive and the inks used are non-toxic.  Fit the bottom of the cage with several layers of newspaper at a time, and remove one layer each day, uncovering a fresh, clean layer.  You can stack a couple week's worth of paper in the tray, which will save you time.  The easiest way to fit the newspaper is to lay out several pages on the table, squaring up the corners.  Place the tray on top of the stack of papers, lining up the edge of the tray with the edge of the papers.  Tear off the excess paper, pulling it against the tray edge to tear it straight.  You can tear several sheets at a time, and only have to tear two sides if you line up the other two edges with the outer edges of the stack.

Since my cage trays are a bit flimsy, I cut a piece of lightweight paneling to the size of my tray and use that as my template.  This actually works better because I can stack more layers of newspaper beneath it to tear.  The rigid, sharp edge of the paneling makes tearing easy.

Tearing cage paper using a template.

I've seen people use small animal bedding for floor covering, but don't think this is the best practice.  It holds moisture and can mold if not changed frequently, and you can't be as observant of the birds droppings as you can if you are removing soiled newspaper daily.  Changes in a bird's droppings will give a warning that the bird may be sick.

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