The busier the pattern on your paper, the less obvious any rips or piecing. Plain, rough papers can be ripped (not cut) and applied piece by piece for an interesting look.
Combinations of different shades of color are especially pleasing, such as complementary red, orange or purple hues.
If you are cutting out highly detailed images, such as flowers, you don't have to cut precisely - wide outlines look fine.
The heavier the paper, the longer you must hold it down to make sure the glue sticks. Tissue paper gives the quickest grip, but also rips easily.
Beware of placing a decoupaged object on newspapers to dry; the newspaper edges can blow against the wet polyurethane and leave indelible black ink spots.
If you mix paint colors to paint backgrounds and trim on decoupaged items, save leftovers in small glass jars. During the decoupage process, the extra paint will come in handy for unexpected touchups or coverups.
If papers rip a little, don't despair. Magic marker pens can fill in a multitude of gaps. Look over the whole decoupaged item, making touch-ups, before applying the first coat of polyurethane.
Don't forget that polyurethane comes in spray cans - perfect for use on small decoupaged items and no paint brushes needed.