I'll try to do it really quick and if you have questions, we can go from there.

In both cases, the tubes are cut so that they fit snuggly together. The cuts are called miters. You can see how the cuts are shaped if you look at a welded frame.

Lugs are steel 'sleeves' that then fit around the joint. They look like this:



The lug is the curvey bit.

Lugs are brazed into place. It's a process that's not unlike how copper pipes are joined to supply water to your house. You put flux on the outside of the tubes and the inside of the lug. Then you heat the whole thing and when it gets hot enough, you introduce brass or silver solder and capillary action draws the liquid solder into the gap between the lug and tubes.

Welding it usually TIG welding. The tubes are cut and fit VERY carefully and then welded. Filler rod of a similar material is used.

Don Walker is a regular poster on this forum. He builds custom frames. Look for one of his postings and contract him. And tell him Matthew sent you.