Here are some things to get you started with button making for 1550-1650. I will mention that metal and glass buttons were also used, but here I will focus on passementerie or textile worked buttons.
The complete class notes / slides from the button class I taught at Jamestown are available at the links above and provide the best overview of the button types and what's appropriate for each.
I highly recommend checking out Gina Barrett, particularly her book Buttons: A Passementerie Workshop Manual which has the best instructions I've found for how to make buttons. She also runs a Facebook group, Gina-B Silkworks Group where you can see what others are making and she even has a Youtube channel with how-to videos. My only complaint is that she doesn't provide a lot of details on the historical aspects, like what buttons are appropriate for a given time period (though I have heard she is working on another book that may cover this).
In order to understand the historical context, I've been collecting a list of buttons from 1550-1650 and as many pictures of them as I can. I also collect how-to illustrations for button making.
I generally group the buttons for 1550-1650 into 4 main categories: Turks Head, Ribbed, Woven and Buttonhole.
Turks Head
My chevron / turks head category includes buttons based on a foundational turks head knot. They are the most common, though most of the examples that remain to us are fancy, upper-class specimens. I find these the most difficult to make.
They are generally made over a wood core and mostly spherical in shape. See pics.
Ribbed
The next most common are the ribbed buttons. This category includes many variations and are relatively easy to make. Though the techniques to make them may differ some, each are characterized by noticeable ribs from the top to the bottom of the button.
They are generally made over a wood core and mostly spherical in shape. See pics.
Woven
The third major grouping are the woven buttons. This includes even-weave and basket-weave.
They are generally made over a wood core and shaped like a flat dome. See pics.
Buttonhole
These buttons are not as common, but I still found 5 examples. They have a foundational wrapping to anchor the buttonhole stitches.
They are generally made over a wooden core and mostly spherical in shape. See pics.