The performer takes a newspaper and forms it into a cone. He shakes it gently and flowers begin to appear — more and more until they overflow all over the stage.
The newspaper is perfectly ordinary and can be opened and shaken before being used, to show the audience that it is in fact innocent. The flowers are the trick: they are artificial and made to order.
The flowers are made of fine tissue paper, colour to suit, and have four petals, glued together at the base on one side, but on the other only the two inside petals are glued. A very light metal expander (D in the diagram) consisting of two curved pieces fixed together at the base, and coloured to match the flower, is attached by gummed paper to the outside two petals. A hundred or more such flowers are bundled together by a thread or rubber band; the resulting bundle (C in the diagram) is small enough to be palmed easily; when then performer has made up the newspaper cone, it's then simple to remove the thread or rubber band and flip the bundle into the cone; the flowers will then open by themselves and crowd each other out as per the described effect.
If the performer wishes to pass the flowers off as real ones, s/he'll have to keep the audience at a little distance; but as part of the effect is the sheer quantity of flowers, s/he may want to emphasize that instead. In this case, so long as no-one is close enough to observe the palming and manipulating of the bundle, spectators can be quite close.
Assistants that incur the displeasure of the performer can as a penance be directed to prepare the bundle!