If you've never made a paper toy before, you can be sure to run into a few snags along the way. The good news is, it gets easier (and the results get prettier) with each attempt! Hopefully the following tips will help speed up the learning curve:
1) Don't print the template on an inkjet printer!
Color inkjet printers have become cheap, meaning that almost everyone's got one in their home or office. The problem is, if the printed ink comes in contact with even the slightest moisture (a droplet of water, oil from your hand, that bit of leftover food you missed on the kitchen table), it smears and smudges, leaving an awful mark on the template that you'll never be able to fix. For this reason, I recommend taking the template files to a professional printer shop and printing them on a laser color machine using card stock (non-gloss) paper. This will result in a crisp, professional printed template that'll last the process of construction and display.
As for printing paper, I recommend using cardstock paper, non-gloss, with a weight of 200-250 g/m2 (grams per square meter). If you can't find this exact paper, ask the print shop/office supply shop what they recommend.
2) Print an extra...or two...
If this is your first time doing a paper toy, don't expect to get it all right the first time. It's a practiced skill. I recommend printing 2 or 3 sheets your first time around, just in case you run into some issues the first time around.
3) Use an X-acto (or other sharp razor knife), not scissors!
With the exception of the occasional rounded cut (which I normally try to avoid in my templates), X-actos are a much better tool for cutting than a pair of scissors. When used with a straight-edge (preferably a ruler), X-actos will give you a perfect, clean edge that you'll never get with a pair of scissors.
4) Use Elmer's (or other water-based glue), and just a bit!
After much trial and error, I can definitively say that Elmer's is the way to go. So resist the urge to use the kids' rubber cement or that half packet of superglue lying in a drawer somewhere. Those glues will result in a sticky mess! Since you usually only glue the flaps of a template, you'll only need a tiny dot of Elmer's. Once the sides are stuck together, you'll have 30 seconds or so to slide things around to get a perfect fit before things dry and stiffen.
5) The importance of scoring
Scoring is a crucial part of building a paper toy, and the result will absolutely be ruined if it isn't used. Using the back of the razor blade against a straight edge, run the blade firmly (but not to the point of tearing) against the line you want to score. If you use the front of the blade, you'll cut the paper, but the back of the blade creates a deep crease that makes folding a breeze later on.
6) Keep the blade sharp
X-acto blades dull faster than you might think. Before you start a new project, always replace the razor tip. A dull blade will increase your likelihood of having to cut twice, which creates a myriad of other problems. Use a sharp blade, change it often, and only cut once. (Also, be safe about disposing old blades. And never leave them lying on surfaces or the ground, especially if you have pets or little children.)
And that's it! You'll probably learn other tricks and methods along the way, but these should be enough to get your started with making some super cool paper toys. Enjoy!