How are headers soldered in PCB assembly?

You don't necessarily have to do wave soldering for the THT parts. There's a technique called THR (through-hole reflow) that works for certain components like connectors. Basically the holes get filled with paste (e.g. by dragging it into the hole with a squeegee-like device) and then the pin is inserted in the pasty hole. So this method is also called "pin in paste".

There are even detailed guides for caculating precisely the ammount of solder paste that's needed for this kind of THR process. More on THR/pin-in-paste in this Littlefuse appnote, which focused on [their] fuses used that way though.

Yet another name/acronym for this is PIHR (pin-in-hole reflow). Worth mentioning because the guys using/promoting it wrote extensively about it. And I can [partly] answer the question from the comment[s] from there: "The first presentation on the subject was by Racal at Nepcon West, USA in the late 1980s. Unfortunately, the paper was never published." I don't know when it became more widespread though.

Also there are some small scale (still four figures in cost) ovens and stencils (+squeegee) compatible with this THR process; an example I know about is sold by eurocircuits, which also has some tips on using THR with it. Most of the tips would apply to any other small oven used for THR though.

If you mix SMT with THT , you may need to do wave soldering after reflow soldering for 1sided boards. One way to avoid this is to assemble pin in paste connections by design. Hole size and paste aperture size are selected to reflow the THT header at same time as SMT parts. Consult with Process Engineers for best results.