How can I cover a large posterboard with glitter?
If you want the poster to be solid glitter, not simply speckled, I would use a spray adhesive, which is best with large surfaces. It also will not add additional weight or bow the the poster like a liquid or paste glue. 

Spray adhesive and glitter are extremely messy. Work outside with plenty of ground cover (I suggest paper) and a large over-spray zone (don't spray near cars, etc.). 

I recommend working the entire surface of the poster at once and not in sections. Previously glittered sections will get over-spray and you'll end up with sections of the poster with thicker layers of glitter than others.

The key to doing the whole poster will be to follow the directions on the spray glue can and to get a good solid covering of glue on the entire surface before applying glitter. 

You'll need to literally dump a pile of glitter on the sticky poster, pick up the poster and shake the glitter around like you're shifting for gold. When the surface seems covered, turn the poster up facing you and tap the bottom edge a couple of times on the ground to release extra glitter. You should get a good view as to how well it's covered. 

Above all, test your technique! Get a second poster, cut it in quarters, and begin testing your technique until it works the way you want.