In the early 1900s when I was a child, my father kept his shaving equipment in the sink alcove in the scullery.
The shaving equipment consisted of a shaving brush, a specially shaped china shaving mug and a razor.
The shaving mug held the hot water and the lip of the mug held the soap.
Shaving could be a tricky business because the razor had an open blade which had to be kept very sharp. When it wasn't in use, it folder inside its handle, as shown in the photograph, but it could still needed to be treated with care.
The blade was sharpened on a special leather strap called a 'strop'. This had a fine powder applied to it to act as an abrasive. Both sides of the blade had to be stropped.
My father would use the brush and soap to work up a thick lather around his chin and then contort his face and use his hand to stretch his skin.
Then, as he drew the blade of the razor over it, only the stubble would be cut and not his face. It was, though, quite common to see men with cuts on their faces from shaving.