Matthew Carter was first introduced to type by his father, who was himself a typographer and book dsigner.
After leaving school, Matthew Carter spent a gap year at the Enschedé type foundry at Haarlem in Netherlands. He learned how to make type by hand, using steel cutouts and matrices for casting lead type.
Five years later he moved to New York. His time here lead him from being a type-setter to a type designer.
He then moved back to London, working on several typefaces including one that was used at a new terminal at Heathrow Airport. After a few years as a freelance typographer he moved back again to New York to work for Mergenthaler Linotype.
In 1971 he moved back to London (again) and for 10 years worked as a freelance designer continuing to produce work for Linotype companies. It was at this time that he designed Bell Centennial for AT&T. It is used by the company in their phone books.
One of his most recognised works in the typographic community is Verdana. It was designed for Microsoft for use in applications such as Word and being the main font used in web browser such as Internet Explorer.
In the film Helvetica, he describes his process for making fonts. He says that he starts with a lower case ‘h’ as this gives him many different aspects to work with - things such as stem height, x-height, weights, widths, terminal properties (i.e, flat/rounded/angled) and serif properties (if it’s a serif typeface). From here he can design letters such as ‘n’, ‘m’, ‘u’, ‘r’, and can combine it with letters such as ‘o’ to form a ‘d’, ‘b’, or ‘p’.
I’m using this process myself when designing my own typefaces.