There are several methods: traditional, using lugs, brazing with brass, and TIG welding. Each of them has its advantages and disadvantages.
In both TIG welding and brazing, precise fitting (cutting) of the tubes being joined is necessary.
Brazing involves joining tubes using melted metal: brass or, in the case of small or stainless steel elements, silver solder. Brazing is done using an acetylene-oxygen torch. The surfaces being joined must be very clean and additionally covered with a special flux that protects the joint from oxidation. Only the material joining the tubes is melted, the tubes themselves are not. The advantages of such joints are aesthetics and easier connections than when using a welder. The disadvantage is the need for fairly laborious cleaning and leveling of the joints. Cleaning and grinding the joints in one frame can take even a few days!
TIG welding, on the other hand, involves creating a weld using an electric arc that melts the edges being joined. Additionally, material is added (in this case, steel rod). All of this is done under the cover of inert gas, in this case, argon. This method is more difficult than brazing because it requires watchmaker precision. This precision comes only with a lot of practice and experience.
Connections made both by TIG welding and brazing have absolutely sufficient strength, significantly exceeding the strength of the steel tubes themselves.
Lugs are heavier than the two above solutions. Additionally, in the case of using ready-made castings, they limit the possible angles of joining and tube diameters. They facilitate the production process, however, and can have remarkable aesthetic qualities.
The above description is a brief explanation of why making a custom frame by hand takes so much time. And, as a result, it also has to cost a lot – often significantly more than an entire ready-made bike from the mid-range.