The electrodes are made of graphite and the lining of the furnace is lined with a ceramic material. Both have melting points higher than the molten steel.
and if you (OP) continue asking "well how was the ceramic material made?": it is produced by dry dust pressing.
Consumable graphite electrodes.
(edit: also, there are plenty of materials that can deal with sustained molten steel content with acceptable service life.)
There's an xkcd what-if that says, paraphrased, "little is known about the properties of molten tungsten, because -- and this might sound stupid -- we don't know how to make a container that will hold it".