Here's how i've built my 2 $ mallet.
It's a cheap and easy project that involves basic tools and the result is very nice.
You can follow my instructions and/or watch the video for the details.

Step 1: BOM and Intro

I don't have a lathe and i didn't want to use a lot of time to build a good looking handle, so i've considered buying one, it was 2$ on a DIY center, and it's very nice and made out of hickory wood.
And that was about it!
The rest was scrap wood that i had lying around in the shop.
The beauty of mallets is that they are simple yet essential tools, and you can build one made out of whatever you like.
So i had those scraps of 14 mm thick azobe wood (they sell it as hard wood in every DIY center) in the shop, and i decided to glue 4 of them, but you can use whatever you like and achieve the thickness and lenght you want. Bear in mind that of course pine wood will make your mallet very soft and less durable.

Step 2: Cut and Paste :)

The first step is to cut to size the scraps. I've cut them square as well, but that's my preference, you can make your mallet with an angle if you wish. Something like this \---/ is what is common to see.
As i said you will require only basic tools, so instead of a miter saw, a hand saw will work the same.
Then you have to glue them up, spreading the glue carefully, and clamp them up waiting for the glue to set.

Step 3: Shaping and Rounding the Edges

At this point you can quicly give a shape to it and smooth up the edges if you like, with a rasp. I've used a Stanley Surform, which worked flawlessly.
Also in my video i explain a nice filing technique to get perfectly round edges.

Step 4: Drill Some Holes

I've found the center of the top part and traced the contour of the handle top.
Then, since the handle is tapered and the section is not uniform, i've traced the shape on the side of the mallet so i could follow it when drilling, then started drilling with a 4 mm bit all around the contour (inside).
After that i've drilled a hole in the center with a 14 mm bit.

Step 5: Filing and Filing and Filing

Now you will have to patiently file away with curved and circular rasps, until you get to the point that the handle will fit in.
My suggestion is to start from the top and file straight until you touch the contour of the handle top, then work your way to a larger contour on the bottom.
Be carefull, and test fit often.
This is the most tedious part. If you don't like to file, you can go for a non tapered, uniform thickness handle, which will ease this part a bit.

Step 6: Fitting and Filling the Gaps

The final fit should be quite tight. You should infact be able to push the handle in by hand up to the last 10 mm or so.
Then drive the handle in with something ( a rubber hammer or... another mallet? :D )
The top and bottom contours, unless you are a robot, will have some gaps. In my case they were a couple of millimeters, and thats because that are the point where you get in and out with the files, but the fit was tight.
To fill that gaps i've mixed some sawdust with wood glue, and filled them up.
When the mix was dry, i've sanded it and it looked nice and smooth.

Step 7: Dowels

Now i've marked 2 spots 15mm from the top and bottom of the mallet, and drilled two 10 mm holes for the dowels.
I've cut 2 dowels slightly longer than the mallet width, put some glue on them and then jammed them in the holes.
If you don't have dowels, and want to stick to the 2 $ budget you can use whatever piece of wood with square or rectangular section. Just drill a hole and then square it up with a chisel (be careful and precise).
It's not as elegant but you can also actually use 2 screws or even nails.
Or ultimately buy the dowels, it will only add barely a few cents to the total cost.

Then i cut the dowels almost flush with a small hand saw. Careful not to cut parts of the mallet when you do this.
Then make them flush with a chisel. Don't drive the chisel straight into the dowel as this may crack them or give a bad finish to them.
Enter the chisel in the dowel at an angle, and give it a slicing motion.

Step 8: Sanding and Finishing

I've sanded down with 180 and then 240 the whole thing, also the handle, so i could get rid of the printed barcode and the old finish.

Then i've applied boiled linseed oil to it for a nice finish.
TIP: old socks work great for this :)

End. Hope you enjoyed my instructable and will try to build it.