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(I know the evidence for early medieval Europe; I can't speak to the late medieval iron economy - post 1000 - with as much confidence.)

In early medieval Europe, smelting sites are usually separate from blacksmithing sites (except in very high-status sites where both types of production occur).

How exactly the iron produced at smelting sites was distributed, in the early middle ages at least, is still not entirely clear (though people have been trying to answer the question for some time). R. Pleiner has argued that the iron was traded, perhaps even as a currency substitute (Pleiner 2006), but the archaeological evidence is ambiguous and F. Curta has suggested that the archaeological evidence actually suggests centralized production for tribute from smelters to local elites. Most likely, both processes were at work: iron smelting sites are frequently found near high-status sites (like the palace and monastic site in Lyminge, Kent), and moved outward through trade networks that were in some way connected to this local authority. The large smelting centers in early medieval scandinavia and Poland were likely producing metal for a larger market beyond local needs, but whether through trade or elite exchange is (again) not yet known (this is part of a larger debate about whether early medieval exchange was market-based or more of a command economy that is far from ending).

There's also evidence suggesting that, on a local level, some smelters were itinerant, visiting local communities to direct smelts every year. This local production is harder to spot archaeologically (because isolated smelting furnaces are hard to spot), but more and more evidence of these rural productive economies is being discovered.

Blacksmiths could also recycle iron. R. Fleming (2012) has argued that, in early medieval Britain, there was a huge quantity of Roman iron left in abandoned villas and military sites. There's a lot of evidence of recycled metal being used in weapons from the period.

We have more evidence for blacksmithing in the early middle ages. Basically every settlement site in England has slag from blacksmithing (Hamerow 2012), though it's not always clear whether these smiths were permanent residents or itinerant between several local communities. There's a bit of textual evidence that refers to smiths: some laws refer to slaves who were trained blacksmiths, and there's the story of Weland who was deliberately crippled to prevent him leaving the king for whom he was forced to smith, which may suggest that some elites tried to prevent good smiths from leaving; but these sources are not particularly informative.

For a good overview (if you can track down a copy): Radmir Pleiner, Iron in Archaeology: Early European Blacksmiths, (2006). Pleiner also has a 2000 book on smelting that discusses some of these questions.