As a Wilton Instructor, this is what we use for constructing ours. Pretty much the same as the other posted, but this one used meringue powder, found at stores which sell cake decorating supplies (also, Wal-mart carries it). With meringue powder, you are able to rebeat and reuse it at a later time, not so with the egg white.

ROYAL ICING

3 level TBSP. meringue powder
1 lb. sifted confectioners sugar (use pure cane)
5-6 TBSP. lukewarm water

Combine all ingredients. If you're using a hand-held mixer, beat 10-12 minutes at high speed. With a heavy-duty mixer, beat 7-10 minutes at low to medium speed. To prevent drying, be sure to cover the bowl with a damp cloth while working with icing. Store in airtight container for up to 2 weeks. To reuse, beat it to restore original texture.
(Make sure beaters and bowls are grease-free and if using a hand mixer, if it gets too hot before the 10 minutes are up, turn off the mixer and cover the bowl and mixer with a damp towel, then when mixer is cooled off, finish up the time.)