Vegan baking is tricky, and it takes practice. Don't get discouraged if things don't turn out right the first time (or even the second or third time)! Believe me, I've thrown away my fair share of awful "cookie" lumps.
Some of the most common ones are:
1/2 banana = 1 egg
3 Tb. applesauce = 1 egg
1/4 c. blended soft tofu = 1 egg
1 Tb. ground flax seeds (or 2 Tb. flax powder) + 3 Tb. water = 1 egg
1/4 c. soy yogurt = 1 egg
Just remember that the banana and applesauce add a slight fruity flavor while the ground flax seeds are kind of granola-y (best for whole grains breads and such).
This link takes you to the Post Punk Kitchen website. It contains more info on how to make those delightful vegan substitutions you want to learn so much!