How do I get a delve boss to spawn?

[Itzgeez]

Do I just wait nearby or can I speed the process?

[quarre]

Just wait few minutes.

If you're asking about Cyrodiil delves, there's some delves where resp only one boss at time, even if cave has few bosses on map. Resp is random, can be same boss few times in row, ez. So you can kill time by grinding on mobs. Cyro delve bosses resp timer is ~10 minutes.

[Drake]

Delve boss timer is 5 minutes, it can be less if more people enter the delve, but be aware that your personal timer is still 5 minutes. So don't kill the boss even if it respawns before 5 minutes, you won't get any loot from it.
The same applies to public dungeon bosses and world bosses, the only difference is the time.

If you're farming I would consider using a timer or alarm clock mod that you can set and reset so that you know when to go back to the boss.