You will need to begin a collection of small to tiny doll buttons. You can begin by collecting the smallest sewing buttons you can find. Check your local fabric shops and look at ones meant for children’s clothes. For larger dolls, these may be quite fine for dolls such as Cissy, Tonner American Models, or 60 cm BJDs and larger. For very small dolls, you will have to search for places that specialize in doll supplies. Do a search - there are many of these places on the internet these days. Another good place to check is Etsy.
You will need a place to store all your doll buttons. I store mine in small jewellers boxes. These are small, round tins with a glass top, which is really handy to be able to see what buttons you have. They come in flat metal boxes, which are handy for storing the button containers. Other possibilities are small jars, pill bottles, or other small containers.
Whatever you choose, be sure you can keep your collection straight and that you can see what you have. There is nothing so frustrating as having to open all sorts of containers just to find what you are looking for!
To attach buttons on doll clothing, it is very difficult, except for the larger dolls, to open and close them with an actual small button hole. I've been able to sew small button holes for some of the larger dolls. It depends entirely on how good you are at making buttonholes! Some sewing machines will let you made a very small button hole, suitable at least for children's buttons - if it is in scale with your doll, see if this will work for you. Otherwise, you could sew the buttonhole by hand. Hand sewing is most appropriate when you are sewing for antique fashion dolls, such as Huret or Doleac dolls.
For most small fashion dolls, the buttons are not functional. They are just sewn on over a snap (press stud), which is sewn on underneath and actually holds the garment closed. This way of attaching the buttons keeps the garment looking in scale and eliminates the need to hassle about with tiny little buttonholes.
Another way to close a doll's garment with buttons is to sew a thread loop. This is the preferred way to attach buttons and close them for antique and reproduction antique dolls. You can sew the loop with either a chain stitch or by sewing several larger stitches in the same place and then sewing a button hole stitch along the length of the stitches. This is fairly easy to do and looks, not just very nice, but authentic for reproduction antique doll garments. But it can also work well for modern doll clothes.
Whatever you do - remember! Keep it in scale!