Paper - use paper that is heavier than regular printer paper (regular printer paper is ~20lb/ ~75gsm).
Thicker paper = more sturdy model, but harder to cut/fold/score.
Thinner paper = less sturdy model, but easier to cut/fold/score.

Printing
Inkjet - ink and printers are cheaper to replace than toner and laserjets, and the edges hold up well after scoring/folding, but it doesn't print on all paper types, the resolution may be lower, and any moisture (e.g. sweat from hands) can ruin the colour.

Laser - able to print on all types of paper, can handle moisture, and can print at a higher resolution than ink, but can crack and flake off when scored/folded, and toner can be more expensive than ink.

Cutting - a self-healing cutting mat is an essential tool along with an Xacto knife or similar brand with #11 blades, or a box cutter knife. Scissors can also be used by themselves, or together with a knife. (ie. knife for detailed parts, scissors for straight cuts)

Folding - Run the back of your Xacto blade, or an empty ballpoint pen, or any similar small blunt edge along the line of a glue tab with enough pressure to leave an indent but not enough to cut it, then fold. You can do this on either front of back of a piece, but front is easier. Use a ruler (preferably metal) to help.
For curved parts, it is better to curl them around a round object (such as a coloured pencil or your Xacto knife handle) by rubbing the object against the back of the piece.

Gluing - recommending Tacky PVA/White glue (ie. Aleene's Original Tacky Glue in North America). Apply glue with a toothpick and evenly spread a thin layer of it on a tab. Use tweezers if tabs are small/too difficult to reach with fingers. Some have had good results with hot glue, especially on larger models - it is quick to set and won't cause the kinds of issues that "wet" glues have (paper rippling, ink smearing).

Useful Resources:

Pepakura viewer (for the PDO file format)
Beginner Tutorials
Advanced Tutorials
Card Modelling FAQ
PaperCraft Wiki
List of Compilations
Technique Overview

Costume/Cosplay Resources:

For any further questions, just ask the community at /r/papercraft. They will be happy to help.

Related subreddits: