Doilies - I recommend getting more than you think you might need. Balloons are big, and it's nice to have flexibility with where you place the doilies on your lamp. I found all of mine on Ebay (search for lot sales of doilies, and you'll find a lot of options), and I'll bet yard and estate sales would also have plenty.
Wallpaper glue - After a few tries with different glues, I can confidently say that wallpaper glue will be your best choice. I found a powder at my local hardware store, and mixed it much thicker than the directions stated, so it had a slightly-more-liquidy-than-jello consistency. On my first try I used a watered down wood glue, and this proved to be too sensitive to a humid environment. After 1 night of San Francisco fog and open windows, it collapsed on itself. Not cool.
3 ft round balloon - Sizing is optional, but you don't want the lampshade to run too close to the bulb itself. I recommend using a cold energy-efficient bulb, and not to risk any burning or melty glue. If you can't find a 3 ft balloon at your local party store, they're easy to get online. Round balloons tend to be thicker (read: stronger) than the standard oblong balloons, and so are less likely to pop. But might as well get 2...and not risk it.
Large paint brush - one that you won't mind getting a bit gluey
string for hanging - and some apparatus to do so. I used a ladder.