Welding is the joining of metal of the same or similar kind such that there is no joint or seam: the pieces to be welded become a single piece.
A modern blacksmith has a range of options and tools to accomplish this. The basic types of welding commonly employed in a modern shop include traditional forge welding as well as modern methods, including oxyacetylene and arc welding.
In forge welding the pieces to be welded are heated to what is generally referred to as "welding heat". For mild steel most smiths judge this temperature by color: the metal will glow an intense yellow or white. At this temperature the steel is near molten and just short of combustion.
Any foreign material in the weld, such as the oxides or "scale" that typically form in the fire, can weaken it and potentially cause it to fail. Thus the mating surfaces to be joined must be kept clean. To this end a smith will make sure the fire is a reducing fire: a fire where at the heart there is a great deal of heat and very little oxygen. The smith will also carefully shape the mating faces so that as they are brought together foreign material is squeezed out as the metal is joined. To clean the faces, protect them from oxidation, and provide a medium to carry foreign material out of the weld the smith will use flux -- typically powdered borax, silica sand, or both.
The smith will first clean the parts to be joined with a wire brush, and then put them in the fire to heat. With a mix of drawing and upsetting the faces will be shaped so that when finally brought together the center of the weld will connect first and the connection spread outward under the hammer blows, pushing the flux and foreign material out.
The dressed metal goes back in the fire, is brought near to welding heat, removed from the fire, brushed, flux is applied, and it is returned to the fire. The smith now watches carefully to avoid overheating the metal. There is some challenge to this, because in order to see the color of the metal it must be removed from the fire, and this exposes the metal to air, which can cause it to oxidize rapidly. So the smith might probe into the fire with a bit of steel wire, prodding lightly at the mating faces. When the end of the wire sticks the metal is at the right temperature (a small weld has formed where the wire touches the mating face so it sticks).
Now the smith moves with rapid purpose. The metal is taken from the fire and quickly brought to the anvil; the mating faces are brought together, the hammer lightly applying a few taps to bring the mating faces into complete contact and squeeze out the flux, and finally returned to the fire again.
The weld was begun with the taps, but often the joint is weak and incomplete, so the smith will again heat the joint to welding temperature and work the weld with light blows to "set" the weld and finally to dress it to the desired shape.