For easy models like the Hatsune Miku, scissors, glue, and computer paper will work fine. If you want to make more challenging papercrafts, you’ll need to invest in a few items:

1) An X-ACTO knife/hobby knife or a break-away blade for precise cutting.
2) A rubber cutting board.
3) 80-110 lb. Cardstock. Regular computer paper is really flimsy and you don’t want your painstakingly made models to collapse from weak paper.
4) You’ll need a ruler and (fairly) sharp edge to score the paper. I use the tip of a mechanical pencil.
As for glue, basic white school glue works fine. I personally use craft glue, but as long as you let ecerything dry, it should be just fine.

When building the papercraft, make sure to take your time. Cut out, score, fold, and glue slowly. I’ve messed up the most basic models from stupid mistakes from rushing.

And last, I’ll leave a few links.

http://papercraft.wikidot.com/papercraft:snake-in-a-box
Contains Snake in a Box, an easy and cool papercraft.

http://members.home.nl/saarloos/
Ninjatoes’ papercraft webpage. It’s got some great papercraft, although much of it is pretty advanced. I’d advise to steer clear of the Final Fantasy and Zelda models until you have some experience.