I don't feel I posess the expertise to give your question the answer that it deserves, but I want to recommend this article written by Craig Johnson.

The other source that I remember discussing late medieval metallurgy in detail is Alan Williams's The Knight and the Blast Furnace, although Williams focuses mainly on developments post-1500, which is rather later than your question speicifically asks for.

My understanding: In the 1300s 1100s (12th century), blast furnaces were just beginning to be used in Western Europe. nearly all iron was produced via the bloomery process, in small batches of 1-5 kg. The bloomery process would remain the predominant method of iron production in much of England until well into the 15th century. Blast furnaces wouldn't be introduced until the 1300s and wouldn't become common until well into the 13th century.

The bloomery process of iron smelting worked something like this:

Finely-crushed iron ore and charcoal are layered in an oven made of clay or soil with a opening at the bottom to permit fresh air to enter. The charcoal was made from wood in this period -- fossil coal wouldn't be used for metallurgy for another century. The stack of raw materials in the oven was then set alight. The burning charcoal would reduce the iron oxides in the ore, and the exhaust gasses would escape out the top. Bellows could be used to increase airflow through the furnace, increasing the temperature and resulting in greater efficiency or iron production. I don't know if limestone fluxes were used, although I would assume they were. This process didn't really get hot enough to fully liquify the iron, and the result was called a "bloom" of "sponge iron". This "sponge iron" was mixture of metallic iron and silica-rich slag, along with rather too much carbon (4%+). The sponge iron would then have to be heated until red-hot then laboriously beaten with a hammer to expose and burn off the extra carbon, and to try to physically work out the silicate impurities (slag). After being worked (sequential heating, hammering, turning, repeat) by a smith, the iron would be wrought iron, with a low carbon content, but still rather more silica than would be considered ideal by modern standards, so medival iron tended to be heteroenous and "streaky" by modern standards. This part of the process (called fining) was often done elsewhere than the furnace site, which had to located close to forests for the charcoal.

After all this, the smith had a piece of what is called today "wrought iron". Today means the iron had a very low carbon content (<0.08% by mass, usually) and a relatively high silica content (2%+?). Actual medieval "wrought iron" was often actually a very low-grade steel by modern standards, since hammer-fining isn't very efficient at removing carbon, so the practical result was often a steel whose high silica content helped compensate for the softness of such a low carbon content. I'm sure there were some tricks for further manipulating ratios of carbon or other impurities (esp sulfur), but I don't really know what they were in the late middle ages.

There are obviously a whole bunch of regional and temporal variations on this process described above, such as furnace geometry, fuel placement technique, and so on, that I don't feel qualified to describe. Some fining furnaces in Germany used water-wheel powered trip hammers to smash the ore and to work the bloom, but I'm not certain that those developments had spread to England yet in the 1100s.

To come back to your original question, a castle blacksmith might, depending on location, buy pre-fined wrought-iron/steel bars and work them into tools and goods himself, or he might just purchase a bloom and work it into wrought iron or steel himself. It depended on the relative cost of both fuel transportation locally, I think.

Edits: a ninja did it.