Right, so, a few things to note here:

There are many ways to make an Atlatl, but I noticed that there is a lack of detailed guides out available on how to make any of them. So, this Instructable covers how to make the simplest (yet effective) one possible; You can probably make it in about half an hour, if you have everything needed on hand.
I am in no way, shape, or form an expert on the Atlatl, nor the art of using them. There are whole communities of enthusiasts out there, typically who build their own perfectly balanced masterpieces. I made this in about thirty minutes with a Swiss Army Knife and a little hand saw.
This is my first Instructable.
I'm new to using the Atlatl, so my stance and motions probably look silly to those whom are more experienced, but I was able to achieve consistent accuracy and velocity after only about half an hour of practice.

This is not a showpiece, or a competition quality weapon. This is something that you can make while you're camping, or stranded out in the wilderness surrounded by bears. It's tough, it's accurate, and it's relatively powerful.

With that out of the way, let's get started with what you will need.

Step 1: What You Will Need

An axe. Any size should work, from hatchet, to tree felling.
A multitool, or at the very least a sharp, sturdy knife.
A small saw, which most multitools have included.
Wood, which I'll talk about in the next step.
Eye protection

Step 2: Get Wood

For the purposes of keeping this guide short, I'm not going to teach you how to make your own darts from scratch. Instead, I'll be using a .79 cm x 122 cm dowel rod, which can be bought at most hardware stores.

I'll probably do a separate guide for the darts, because it involves weeks worth of preparation to ensure they come out straight.

How to pick out the wood you will use for your Atlatl:

If you are going to do it the hard way, you'll want to look for saplings that are about an inch thick. After you find one, cut it down, strip the branches away, and only keep the thickest and straightest segment, which is typically towards the base of the tree. I'd suggest leaving your new stick in its bark for at least a week while it dries out; If you peel the bark off and carve your Atlatl the day you cut it down, it WILL NOT hold it's shape for very long, and it will crack.

Regardless of whether or not you're cutting down your own wood, or buying some at a hardware store, you're going to need roughly 24 inches of straight wood. That is the standard length for an Atlatl, although another method of sizing it is to place the stick under your arm pit, and cut off any wood that extends past your wrist, while it's parallel with your arm. Saw off any excess.

Step 3: Carve the Spur

WEAR EYE PROTECTION! Pieces of wood WILL fly up at your eyes

Time to carve out your spur. This is the hardest part of making an Atlatl, but I wouldn't worry too much about making it perfect. Also note that although my Swiss Army Knife has a saw, I decided to use a separate little hand saw.

How to carve the spur:

Pick where you are going to make your first cut. This will be where the tip of your spur will be. I would recommend it being at least an inch away from the top of your stick, but no more than two inches.
Make sure the cut is perpendicular with the length of your stick, as this is the most important part of carving your spur; if your spur isn't pointing straight down towards the length of the stick, you will not be able to properly nock and throw darts. See the graph above.
Begin sawing, but do not go any deeper than about a quarter of an inch down. You do not want to reach the middle of the stick. See picture #1 above.
Make another cut directly below (towards the base of the stick) the first one. This will make it so that you can easily snap a large chunk of wood out. If you can't do it with your finger, you can wedge something in between, and that should snap it. See picture #2 above.
Repeat step 4 until you've cleared out about one and a half inches of wood. You can continue past there if you want your Atlatl to be lighter. See picture #3 above.
Decide where the very point of the spur will be, and saw two slanted cuts away from it at a roughly 45 degree angle. See picture #4 above.
Snap off the excess wood after making the slanted cuts.
Press the edge of your saw against the inside wall of the spur, and hollow out about a quarter of an inch, towards the top of the stick. See picture #5 above.
Begin carving the final shape of the spur with a sharp blade. Be careful not to make the tip too small, as it might break off under the force of throwing a dart.
Clean off any excess wood.

Step 4: Make Your Dart

It's time to make your dart. This is the simplest and fastest way of making a projectile; You're going to sharpen a stick.

Sharpen the stick

This is as easy as it sounds, but still might take some practice. See pictures #1 and #2 above.

Use a sharp blade, and cut away from yourself.
Don't make the point in the very center of the wood; the softest part of a branch is in the very middle. Instead, sharpen it so that the tip is off center slightly. This will make the point harder.

Dig out a notch on the bottom

This is what the spur of your Atlatl will hook into, and is required to nock a dart. There are many simple ways of digging out a notch like this, and several different tools on a Swiss Army Knife alone that can get the job done. See pictures #3 and #4 above.

Don't make the notch too wide, or too deep. Try to match it to the shape of your spur.

Step 5: Have Fun, Safely

Emphasis on safely. Do not use an Atlatl anywhere near children, people, or animals. They are surprisingly powerful, and equally dangerous.

Here are some videos of me learning how to use the Atlatl I made during this Instructable. Like I said before, I'm new to using these things, and I probably look ridiculous to people who are not, but I was still able to use it effectively with hardly any practice.