Thread, just like clothing, comes in 100% polyester, 100% cotton, and Cotton/Poly blends. Polyester thread is thought of to be better to use in diaper making because it shouldn't wick as much as cotton thread will. I recommend 100% cotton OR 100% polyester, the blended threads seem to be weaker. If you're sewing a wateproof All in One Diaper or a Diaper Cover, you'll probably want to use a 100% polyester thread.
There are many types and sizes of elastics suitable for diaper sewing.
There are various trade names of hook and loop, a very popular closure to sew onto diapers. Aplix, Velcro, Touchtape are just a few. You can help keep the hook part sticking longer if you turn your diapers inside out and fasten the hook and loop before washing. This keeps the hook part from collecting fuzz in the wash. Many sew "laundry tabs" by sewing an additional strip of loop next to the hook tab. This way the hook tab may be folded back to keep it from snagging on other items in the wash. You may also turn soiled diapers inside out and fasten the hook to the front loop panel.
Snaps popular for use in diaper making are either made of a plastic or metal. As with all things, snaps come in a wide variety of quality. Snaps also come in a variety of sizes. The most popular sizes for diaper sewing are 16 Ligne and 20 Ligne. The size of snap you use on your diapers is largely due to personal preference. Plastic snaps are very durable and have the added benefit of not clunking or heating up in the dryer. However, they require the use of a Snap Press to apply. Plastic snaps cannot be applied with a simple hammering tool or snap pliers such as the type you might find in a local fabric store. Those types of tools will apply metal snaps. Metal snaps differ from plastic snaps not only in the material they are made with but in their shape. Plastic snap caps have a single prong that must be smashed properly with a Snap Press. Metal snaps can be applied with a snap press as well if you have the right die pieces to do so. Metal snaps have several prongs around the edge of the cap or open ring.
Both types of snaps are perfectly suitable for diaper making. Metal snaps are more readily available to home seamstresses as they can be applied without the investment of a snap press. However a snap press can be used to apply plastic and metal snaps to more than just diapers. Many use it for applying snaps to clothing, bras, purses, bags, and more. Metal snaps come in a greater variety of colors.
The most popular size for plastic snaps is size 20. The most popular size for metal snaps is size 16, though size 20 is often seen as well.
You need four parts to make a complete snap. See photos.
There are a variety of different kinds of machine needles. You should use the appropriate needle for whatever fabric you are sewing.
This is your basic stitch that runs in a straight line.
Most machines allow you to press a button or pull a lever while stitching to reverse your stitching on top of itself to secure loose threads at the beginning or end of a stitch. You can also just narrow your stitching to secure instead of back stitching.
This is a stitch that most sewing machines can accomplish and is commonly used in place of serging when you don't own a serger. Just like its name suggests the stitch zigs back and forth instead of in a straight line. To "fake serge" you can set a wide, close zig zag and sew close to the edge of your fabrics to trap the edges. It won't look as neat as a serged finish, but can be more economical than buying an expensive serger.
Many machines have this stitch but some do not. It looks like a zig zag, but each zig and zag is broken into three little stitches (see illustration). This stitch is ideal for attaching Lastin Clear Elastic.
A machine that cuts, sews, and finishes the raw edge of material. You can see in the photo that using decorative threads in your serger can create quite a pretty finish on the edge of diapers. Diapers shown are courtesy Suzie at Christensen Creations.