Don't worry, it's not as hard as you may think! :)
Mix some white glue with very little water in a pot, just to make it more fluid.
Once you have these 2 things ready, blow up a balloon: this will be the base of your lamp so make it as big as you want, but remember that your lamp will get bigger after you've added pieces of plastic bag around it.
Start gluing your pieces of newspaper on the balloon with the glue you prepared: spread some glue on the balloon, lay your piece of paper on the glue and add some more glue on it. Continue this way until your cover the whole surface of your balloon, one piece after the other.
Once you're done, do at least another two layers to make it hard enough, and let it dry for at least a night.