In what technique medieval book miniatures were executed and are there materials today for doing this?
The drawing of pictures in manuscripts is known as Illumination*

The Wikipedia article on the subject (as mentioned in a previous answer) contains a wealth of information on the subject, including this gif showing the steps:



Image from Wikimedia commons: link

Steps involved (from the image caption):


I. Graphite powder dots create the outline 
II. Silverpoint drawings are sketched (you could use pencil instead here)
III. Illustration is retraced with ink 
IV. The surface is prepared for the application of gold leaf 
V. Gold leaf is laid down 
VI. Gold leaf is burnished to make it glossy and reflective 
VII. Decorative impressions are made to adhere the leaf 
VIII. Base colors are applied 
IX. Darker tones are used to give volume 
X. Further details are drawn 
XI. Lighter colors are used to add particulars 
XII. Ink borders are traced to finalize the illumination


This is the technique used in illumination.

As for the materials, despite your misgivings tempera is actually extremely robust and was used for all miniatures, along with ink and gold/silver leaf. Tempera's resistance should be obvious from the fact that we have many surviving tempera paintings that are hundreds or even thousands of years old.

Tempera can't be stored, but it's easy to make yourself with egg, water and pigment.

The Wikipedia article also contains a list of common pigments used in Medieval times - you can try your hand at making these, or use easily available synthetic pigments.

As a final aside, vellum is expensive and relatively rare these days but it is still available.

*In the strictest sense illumination refers only to pictures containing gold, but in normal usage it covers all drawings of this type.